Femtosecond proton transfer in urea solutions probed by X-ray spectroscopy.

Proton transfer is one of the most fundamental events in aqueous-phase chemistry and an emblematic case of coupled ultrafast electronic and structural dynamics1,2. Disentangling electronic and nuclear dynamics on the femtosecond timescales remains a formidable challenge, especially in the liquid phase, the natural environment of biochemical processes. Here we exploit the unique features of table-top water-window X-ray absorption spectroscopy3-6 to reveal femtosecond proton-transfer dynamics in ionized urea dimers in aqueous solution. Harnessing the element specificity and the site selectivity of X-ray absorption spectroscopy with the aid of ab initio quantum-mechanical and molecular-mechanics calculations, we show how, in addition to the proton transfer, the subsequent rearrangement of the urea dimer and the associated change of the electronic structure can be identified with site selectivity. These results establish the considerable potential of flat-jet, table-top X-ray absorption spectroscopy7,8 in elucidating solution-phase ultrafast dynamics in biomolecular systems.

Tracking Cavity Formation in Electron Solvation: Insights from X-ray Spectroscopy and Theory.

We present time-resolved X-ray absorption spectra of ionized liquid water and demonstrate that OH radicals, H3O+ ions, and solvated electrons all leave distinct X-ray-spectroscopic signatures. Particularly, this allows us to characterize the electron solvation process through a tool that focuses on the electronic response of oxygen atoms in the immediate vicinity of a solvated electron. Our experimental results, supported by ab initio calculations, confirm the formation of a cavity in which the solvated electron is trapped. We show that the solvation dynamics are governed by the magnitude of the random structural fluctuations present in water. As a consequence, the solvation time is highly sensitive to temperature and to the specific way the electron is injected into water.

Tree-Code Based Improvement of Computational Performance of the X-ray-Matter-Interaction Simulation Tool XMDYN.

In this work, we report on incorporating for the first time tree-algorithm based solvers into the molecular dynamics code, XMDYN. XMDYN was developed to describe the interaction of ultrafast X-ray pulses with atomic assemblies. It is also a part of the simulation platform, SIMEX, developed for computational single-particle imaging studies at the SPB/SFX instrument of the European XFEL facility. In order to improve the XMDYN performance, we incorporated the existing tree-algorithm based Coulomb solver, PEPC, into the code, and developed a dedicated tree-algorithm based secondary ionization solver, now also included in the XMDYN code. These extensions enable computationally efficient simulations of X-ray irradiated large atomic assemblies, e.g., large protein systems or viruses that are of strong interest for ultrafast X-ray science. The XMDYN-based preparatory simulations can now guide future single-particle-imaging experiments at the free-electron-laser facility, EuXFEL.

Resonance-Enhanced Multiphoton Ionization in the X-Ray Regime.

Here, we report on the nonlinear ionization of argon atoms in the short wavelength regime using ultraintense x rays from the European XFEL. After sequential multiphoton ionization, high charge states are obtained. For photon energies that are insufficient to directly ionize a 1s electron, a different mechanism is required to obtain ionization to Ar^{17+}. We propose this occurs through a two-color process where the second harmonic of the FEL pulse resonantly excites the system via a 1s→2p transition followed by ionization by the fundamental FEL pulse, which is a type of x-ray resonance-enhanced multiphoton ionization (REMPI). This resonant phenomenon occurs not only for Ar^{16+}, but also through lower charge states, where multiple ionization competes with decay lifetimes, making x-ray REMPI distinctive from conventional REMPI. With the aid of state-of-the-art theoretical calculations, we explain the effects of x-ray REMPI on the relevant ion yields and spectral profile.

xcalib: a focal spot calibrator for intense X-ray free-electron laser pulses based on the charge state distributions of light atoms.

The xcalib toolkit has been developed to calibrate the beam profile of an X-ray free-electron laser (XFEL) at the focal spot based on the experimental charge state distributions (CSDs) of light atoms. Characterization of the fluence distribution at the focal spot is essential to perform the volume integrations of physical quantities for a quantitative comparison between theoretical and experimental results, especially for fluence-dependent quantities. The use of the CSDs of light atoms is advantageous because CSDs directly reflect experimental conditions at the focal spot, and the properties of light atoms have been well established in both theory and experiment. Theoretical CSDs are obtained using xatom, a toolkit to calculate atomic electronic structure and to simulate ionization dynamics of atoms exposed to intense XFEL pulses, which involves highly excited multiple core-hole states. Employing a simple function with a few parameters, the spatial profile of an XFEL beam is determined by minimizing the difference between theoretical and experimental results. The optimization procedure employing the reinforcement learning technique can automatize and organize calibration procedures which, before, had been performed manually. xcalib has high flexibility, simultaneously combining different optimization methods, sets of charge states, and a wide range of parameter space. Hence, in combination with xatom, xcalib serves as a comprehensive tool to calibrate the fluence profile of a tightly focused XFEL beam in the interaction region.

Ultrafast Charge Transfer and Structural Dynamics Following Outer-Valence Ionization of a Halogen-Bonded Dimer.

We study the temporal evolution of the CH2O···ClF halogen-bonded dimer following vertical ionization out of outer-valence molecular orbitals on a femtosecond time scale, employing mixed quantum-classical molecular dynamics simulations. The charge density pattern in the ground state that is suitable for the formation of the ground-state halogen bond can be changed upon ionization. Depending on the molecular orbital that gets ionized, the change in the charge density transiently strengthens or weakens the halogen bond through altering the electrostatic interaction. A transient increase in the halogen bond strength is observed if the ionization enhances the positive charge on the halogen atom provided that the electron donor site possesses some negative charge. The evolution of the system following ionization is driven by energetic stabilization through transferring the electronic charge from the halogen bond acceptor/electron donor (CH2O) to the halogen bond donor/electron acceptor (ClF). The charge transfer oscillations are at the same time governed by the covalent bond vibrations.

Simulated XUV photoelectron spectra of THz-pumped liquid water.

Highly intense, sub-picosecond terahertz (THz) pulses can be used to induce ultrafast temperature jumps (T-jumps) in liquid water. A supercritical state of gas-like water with liquid density is established, and the accompanying structural changes are expected to give rise to time-dependent chemical shifts. We investigate the possibility of using extreme ultraviolet photoelectron spectroscopy as a probe for ultrafast dynamics induced by sub-picosecond THz pulses of varying intensities and frequencies. To this end, we use ab initio methods to calculate photoionization cross sections and photoelectron energies of (H2O)20 clusters embedded in an aqueous environment represented by point charges. The cluster geometries are sampled from ab initio molecular dynamics simulations modeling the THz-water interactions. We find that the peaks in the valence photoelectron spectrum are shifted by up to 0.4 eV after the pump pulse and that they are broadened with respect to unheated water. The shifts can be connected to structural changes caused by the heating, but due to saturation effects they are not sensitive enough to serve as a thermometer for T-jumped water.

Control of Nuclear Dynamics through Conical Intersections and Electronic Coherences.

The effect of nuclear dynamics and conical intersections on electronic coherences is investigated employing a two-state, two-mode linear vibronic coupling model. Exact quantum dynamical calculations are performed using the multiconfiguration time-dependent Hartree method. It is found that the presence of a nonadiabatic coupling close to the Franck-Condon point can preserve electronic coherence to some extent. Additionally, the possibility of steering the nuclear wave packets by imprinting a relative phase between the electronic states during the photoionization process is discussed. It is found that the steering of nuclear wave packets is possible given that a coherent electronic wave packet embodying the phase difference passes through a conical intersection. A conical intersection close to the Franck-Condon point is thus a necessary prerequisite for control, providing a clear path towards attochemistry.

Radiation-Induced Chemical Dynamics in Ar Clusters Exposed to Strong X-Ray Pulses.

We show that electron and ion spectroscopy reveals the details of the oligomer formation in Ar clusters exposed to an x-ray free electron laser (XFEL) pulse, i.e., chemical dynamics triggered by x rays. With guidance from a dedicated molecular dynamics simulation tool, we find that van der Waals bonding, the oligomer formation mechanism, and charge transfer among the cluster constituents significantly affect ionization dynamics induced by an XFEL pulse of moderate fluence. Our results clearly demonstrate that XFEL pulses can be used not only to "damage and destroy" molecular assemblies but also to modify and transform their molecular structure. The accuracy of the predictions obtained makes it possible to apply the cluster spectroscopy, in connection with the respective simulations, for estimation of the XFEL pulse fluence in the fluence regime below single-atom multiple-photon absorption, which is hardly accessible with other diagnostic tools.

Prospects of Using High-Intensity THz Pulses To Induce Ultrafast Temperature-Jumps in Liquid Water.

Ultrashort, high-intensity terahertz (THz) pulses, e.g., generated at free-electron laser facilities, allow for direct investigation as well as the driving of intermolecular modes in liquids like water and thus will deepen our understanding of the hydrogen bonding network. In this work, the temperature-jump (T-jump) of water induced by THz radiation is simulated for ten different THz frequencies in the range from 3 to 30 THz and five different pulse intensities in the range from 1 × 1011 to 5 × 1012 W/cm2 employing both ab initio molecular dynamics (AIMD) and force field molecular dynamics (FFMD) approaches. The most efficient T-jump can be achieved with 16 THz pulses. Three distinct T-jump mechanisms can be uncovered. For all cases, the T-jump mechanism proceeds within tens of femtoseconds (fs). For frequencies between 10 and 25 THz, most of the energy is initially transferred to the rotational degrees of freedom. Subsequently, the energy is redistributed to the translational and intramolecular vibrational degrees of freedom within a maximum of 500 fs. For the lowest frequencies considered (7 THz and below), translational and rotational degrees of freedom are heated within tens of fs as the THz pulse also couples to the intermolecular vibrations. Subsequently, the intramolecular vibrational modes are heated within a few hundred fs. At the highest frequencies considered (25 THz and above), vibrational and rotational degrees of freedom are heated within tens of fs, and energy redistribution to the translational degrees of freedom happens within several hundred fs. Both AIMD and FFMD simulations show a similar dependence of the T-jump on the frequency employed. However, the FFMD simulations overestimate the total energy transfer around the main peak and drop off too fast toward frequencies higher and lower than the main peak. These differences can be rationalized by missing elements, such as the polarizability, in the TIP4P/2005f force field employed. The feasibility of performing experiments at the studied frequencies and intensities as well as important issues such as energy efficiency, penetration depth, and focusing are discussed.

Challenges in XUV Photochemistry Simulations: A Case Study on Ultrafast Fragmentation Dynamics of the Benzene Radical Cation.

The challenges of simulating extreme ultraviolet (XUV)-induced dissociation dynamics of organic molecules on a multitude of coupled potential energy surfaces are discussed for the prototypical photoionization of benzene. The prospects of Koopmans' theorem-based electronic structure calculations in combination with classical trajectories and Tully's fewest switches surface hopping are explored. It is found that a Koopmans' theorem-based approach overestimates the CH dissociation barrier and thus underestimates the fragmentation yield. However, the nonadiabatic population dynamics are in good agreement with previous approaches, indicating that the Koopmans' theorem based potentials are well described around the Franck-Condon point. This is explicitly tested for the ground state potential of the benzene cation employing CASPT2 calculations, for which very good agreement is found. This work highlights the need for efficient electronic structure approaches that can treat medium-sized organic molecules with a multitude of coupled excited states and several dissociation channels.

The fractal geometry of Hartree-Fock.

The Hartree-Fock method is an important approximation for the ground-state electronic wave function of atoms and molecules so that its usage is widespread in computational chemistry and physics. The Hartree-Fock method is an iterative procedure in which the electronic wave functions of the occupied orbitals are determined. The set of functions found in one step builds the basis for the next iteration step. In this work, we interpret the Hartree-Fock method as a dynamical system since dynamical systems are iterations where iteration steps represent the time development of the system, as encountered in the theory of fractals. The focus is put on the convergence behavior of the dynamical system as a function of a suitable control parameter. In our case, a complex parameter λ controls the strength of the electron-electron interaction. An investigation of the convergence behavior depending on the parameter λ is performed for helium, neon, and argon. We observe fractal structures in the complex λ-plane, which resemble the well-known Mandelbrot set, determine their fractal dimension, and find that with increasing nuclear charge, the fragmentation increases as well.

Real-time observation of valence electron motion.

The superposition of quantum states drives motion on the atomic and subatomic scales, with the energy spacing of the states dictating the speed of the motion. In the case of electrons residing in the outer (valence) shells of atoms and molecules which are separated by electronvolt energies, this means that valence electron motion occurs on a subfemtosecond to few-femtosecond timescale (1 fs = 10(-15) s). In the absence of complete measurements, the motion can be characterized in terms of a complex quantity, the density matrix. Here we report an attosecond pump-probe measurement of the density matrix of valence electrons in atomic krypton ions. We generate the ions with a controlled few-cycle laser field and then probe them through the spectrally resolved absorption of an attosecond extreme-ultraviolet pulse, which allows us to observe in real time the subfemtosecond motion of valence electrons over a multifemtosecond time span. We are able to completely characterize the quantum mechanical electron motion and determine its degree of coherence in the specimen of the ensemble. Although the present study uses a simple, prototypical open system, attosecond transient absorption spectroscopy should be applicable to molecules and solid-state materials to reveal the elementary electron motions that control physical, chemical and biological properties and processes.

Towards RIP using free-electron laser SFX data.

Here, it is shown that simulated native serial femtosecond crystallography (SFX) cathepsin B data can be phased by rapid ionization of sulfur atoms. Utilizing standard software adopted for radiation-damage-induced phasing (RIP), the effects on both substructure determination and phasing of the number of collected patterns and fluences are explored for experimental conditions already available at current free-electron laser facilities.

Ultrafast Charge Transfer of a Valence Double Hole in Glycine Driven Exclusively by Nuclear Motion.

We explore theoretically the ultrafast transfer of a double electron hole between the functional groups of glycine after K-shell ionization and subsequent Auger decay. Although a large energy gap of about 15 eV initially exists between the two electronic states involved and coherent electronic dynamics play no role in the hole transfer, we find that the double hole is transferred within 3 to 4 fs between both functional ends of the glycine molecule driven solely by specific nuclear displacements and non-Born-Oppenheimer effects. The nuclear displacements along specific vibrational modes are of the order of 15% of a typical chemical bond between carbon, oxygen, and nitrogen atoms and about 30% for bonds involving hydrogen atoms. The time required for the hole transfer corresponds to less than half a vibrational period of the involved nuclear modes. This finding challenges the common wisdom that nuclear dynamics of the molecular skeleton are unimportant for charge transfer processes at the few-femtosecond time scale and shows that they can even play a prominent role. It also indicates that in x-ray imaging experiments, in which ionization is unavoidable, valence electron redistribution caused by nuclear dynamics might be much faster than previously anticipated. Thus, non-Born-Oppenheimer effects may affect the apparent electron densities extracted from such measurements.

Imaging electronic quantum motion with light.

Imaging the quantum motion of electrons not only in real-time, but also in real-space is essential to understand for example bond breaking and formation in molecules, and charge migration in peptides and biological systems. Time-resolved imaging interrogates the unfolding electronic motion in such systems. We find that scattering patterns, obtained by X-ray time-resolved imaging from an electronic wavepacket, encode spatial and temporal correlations that deviate substantially from the common notion of the instantaneous electronic density as the key quantity being probed. Surprisingly, the patterns provide an unusually visual manifestation of the quantum nature of light. This quantum nature becomes central only for non-stationary electronic states and has profound consequences for time-resolved imaging.

Coherent electron hole dynamics near a conical intersection.

The coherent evolution of an electron hole in a photoionized molecule represents an unexplored facet of charge transfer phenomena occurring in complex systems. Using ultrafast extreme ultraviolet spectroscopy, we investigate the real-time dynamics of an electron hole wave packet created near a conical intersection in CO_{2}. We resolve the oscillation of the electron hole density between σ and π character, driven by the coupled bending and asymmetric stretch vibrations of the molecule. We also quantify the mixing between electron hole configurations and find that the wave packet coherence diminishes with time due to thermal dephasing.

Microscopic nonlinear optical response: Analysis and calculations with the Floquet-Bloch formalism.

We analyze microscopic nonlinear optical response of periodic structures within the Floquet-Bloch formalism. The analysis is focused on the real-space distributions of optically induced charge and electron current density within the unit cell of a crystal. We demonstrate that the time-reversal symmetry of a crystal determines the phases of the temporal oscillations of these distributions. We further analyze their spatial symmetries and connection to macroscopic optical response. We illustrate our study with ab initio calculations that combine density functional theory with the Floquet-Bloch formalism. The calculations provide time-dependent optically induced charge distributions and electron current densities within the unit cells of a crystal with inversion symmetry MgO and a crystal without inversion symmetry GaAs in response to a strong-field excitation. The real-space, microscopic view on nonlinear optical response provides insightful information about the strong field-matter interaction.

Computational study of diffraction image formation from XFEL irradiated single ribosome molecule.

Single particle imaging at atomic resolution is perhaps one of the most desired goals for ultrafast X-ray science with X-ray free-electron lasers. Such a capability would create great opportunity within the biological sciences, as high-resolution structural information of biosamples that may not crystallize is essential for many research areas therein. In this paper, we report on a comprehensive computational study of diffraction image formation during single particle imaging of a macromolecule, containing over one hundred thousand non-hydrogen atoms. For this study, we use a dedicated simulation framework, SIMEX, available at the European XFEL facility. Our results demonstrate the full feasibility of computational single-particle imaging studies for biological samples of realistic size. This finding is important as it shows that the SIMEX platform can be used for simulations to inform relevant single-particle-imaging experiments and help to establish optimal parameters for these experiments. This will enable more focused and more efficient single-particle-imaging experiments at XFEL facilities, making the best use of the resource-intensive XFEL operation.

Attosecond-pump attosecond-probe x-ray spectroscopy of liquid water.

Attosecond-pump/attosecond-probe experiments have long been sought as the most straightforward method for observing electron dynamics in real time. Although there has been much success with overlapped near-infrared femtosecond and extreme ultraviolet attosecond pulses combined with theory, true attosecond-pump/attosecond-probe experiments have been limited. We used a synchronized attosecond x-ray pulse pair from an x-ray free-electron laser to study the electronic response to valence ionization in liquid water through all x-ray attosecond transient absorption spectroscopy (AX-ATAS). Our analysis showed that the AX-ATAS response is confined to the subfemtosecond timescale, eliminating any hydrogen atom motion and demonstrating experimentally that the 1b1 splitting in the x-ray emission spectrum is related to dynamics and is not evidence of two structural motifs in ambient liquid water.