Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which has benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly nonlinear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.

Observing coupled electronic and nuclear dynamics, and the flow of energy between electronic and vibrational degrees of freedom during photochemical reactions, remains a central challenge in ultrafast chemistry. Here, we combine time-resolved Coulomb explosion imaging with ab initio quantum wavepacket calculations to resolve the nonadiabatic dynamics of UV-excited NO 2 as it evolves toward and relaxes through a conical intersection. Excitation at 400 nm, just below the dissociation threshold, launches large-amplitude vibrational motion that explores extended regions of the ground-state potential energy surface following electronic relaxation. Coincident fragment-ion momenta reveal a highly delocalized nuclear wavepacket with correlated bending and asymmetric-stretch motion, providing direct insight into ultrafast vibrational energy redistribution predicted by theory.

Photoinduced ring-opening of cyclic organic molecules is fundamental to many photochemical processes, from vitamin D biosynthesis to molecular optical switching. Despite advances in several ultrafast techniques, direct and unambiguous imaging of the ultrafast nuclear motion is still a major challenge. As a consequence, reaction mechanisms remain controversial even for extensively studied prototypical systems. Here, we show that time-resolved Coulomb explosion imaging, together with molecular dynamics simulation, can be used to identify and map the ring-opening reaction of gas-phase furan following ultraviolet photoexcitation, a reaction for which widely contradicting predictions and observations have been reported. By directly imaging the transient carbon-backbone structure, we reveal the presence of a strong ring-opening pathway that occurs on average at approximately 70 fs. With the development of higher-repetition-rate lasers, we anticipate that our approach will enable mapping of a broad range of ultrafast photochemical reactions.

When matter interacts with energetic radiation it can undergo sudden, or impulsive, ionization. This process can drive chemical change and occurs widely in space and planetary atmospheres, yet its comprehensive description challenges our current theoretical and computational capabilities as it requires advanced treatment of electron correlation and nonadiabatic dynamics beyond the Born–Oppenheimer approximation. Here we measure the response of the para-aminophenol molecule to sudden ionization. Using attosecond X-ray absorption spectroscopy, we resolve the ultrafast dynamics of the ionized molecule with atomic precision. A subfemtosecond decay corresponds to states undergoing non-radiative decay, whereas few-femtosecond oscillatory signatures are associated with electronic wavepacket motion in stable cation states that later couple to nuclear motion. We compare our measurement with state-of-the-art computational modelling, qualitatively reproducing the observed response across multiple timescales. These results provide a benchmark for computational models of sudden ionization and ultrafast charge motion in matter. Impulsive ionization initiates ultrafast electron motion in molecules, but its early dynamics remain difficult to probe. Now attosecond X-ray absorption spectroscopy has been used to track the response dynamics of ionized para-aminophenol.

The trihydrogen cation (H_3^+) initiates the ion-molecule reactions that build molecular complexity in interstellar space. Whether its canonical formation reaction, H_2^+ + H_2 → H_3^+ + H, proceeds on inorganic surfaces under radiation-driven ionization has remained untested. Here we drive H_3^+ formation on hydrated silica nanoparticles using intense 1.88 keV X-ray pulses, combining ion velocity map imaging, electron time-of-flight spectroscopy, and single-particle coherent diffractive imaging to resolve this chemistry on individual particles. The self-induced surface electric field on the V/nm scale drives interfacial charge transfer and water fragmentation. This field is the dominant parameter governing the relative yields of H^+, H_2^+, and H_3^+ across particle size, composition, and aggregation. Density functional theory and nonadiabatic quantum molecular dynamics simulations trace this field-driven charge transfer, directly analogous to band bending at semiconductor photoelectrodes. These results establish surface-field-driven charge transfer as a unifying mechanism between radiation dominated astrophysical environments and field-driven surface catalysis.

Traditional x-ray photoelectron spectroscopy (XPS) relies upon a direct mapping between the photoelectron binding energies and the local chemical environment, which is well characterized by an electrostatic partial charges (PC) model for systems in equilibrium. However, the extension of this technique to out-of-equilibrium systems has been hampered by the lack of x-ray sources capable of accessing multiple atomic sites with high spectral and temporal resolution, as well as the lack of simple theoretical procedures to interpret the observed signals. In this work we employ XPS with a narrow band femtosecond x-ray probe to unravel different ultrafast dissociation processes of a polyatomic molecule, fluoromethane (CH_{3}F). We demonstrate that the PC model can be successfully applied to describe the C-F and C-H dissociation dynamics after strong-field ionization, with excellent agreement between experimental measurements and ab initio simulations. These results enable the application of this technique to out-of-equilibrium systems of higher complexity, by correlating real-time information from multiple atomic sites and interpreting the measurements through a viable theoretical modeling.

Determining the structure and following the structural evolution of molecules undergoing chemical reactions is one of the key goals of ultrafast molecular physics and chemistry. Recently, Coulomb explosion imaging has emerged as a promising technique for imaging the evolving structure of individual molecules in the gas phase. However, its practical application to structure determination is hampered by the lack of suitable algorithms for directly retrieving the molecular structure from the measured fragment-ion momentum data. Here, we propose a scheme to solve the underlying inverse problem by employing neural networks to infer the initial atomic positions from the final ion momenta on an event-by-event basis. Using this scheme, we retrieve the structure of several polyhalomethane isomers from simulated Coulomb explosion imaging data with an average per-atom position error of ∼0.1 atomic units, i.e., to within 5% of the typical bond lengths. This development paves the way for an automated structure retrieval from Coulomb explosion data one molecule at a time, making it ideally suitable for analyzing pump-probe experiments where several products are formed that need to be distinguished.

Time-resolved measurement of Auger-Meitner decay [Drescher et al., Nature (London) 419, 803 (2002)NATUAS0028-083610.1038/nature01143] marked a milestone in the development of attosecond science. To date, the time constants for the Auger-Meitner decay processes obtained from the time-domain experiments were found to be consistent with the values deduced from conventional energy-domain measurements. One of the main factors limiting the temporal resolution of these studies is the unlocked carrier-envelope-phase (CEP) of the laser pulses used to probe the electronic dynamics triggered by inner-shell photoabsorption. In this Letter, we report time-resolved inner-shell electron spectroscopy of xenon and krypton using attosecond soft x-ray (atto-SXR) pulses centered at 130 eV in combination with CEP-stabilized few-cycle Yb laser pulses. We observed that the N_{4,5}OO Auger electrons from xenon exhibit a clear streaking pattern, but with an unexpected time shift of ∼1.32  fs relative to the 4d photoelectrons. Furthermore, the energy-integrated yield of streaked Auger electrons from xenon exhibits a pronounced minimum at a pump-probe time delay of 4 fs. Neither of these observations can be explained by current streaking theories and both are inconsistent with lifetimes inferred from energy-domain measurements. The M_{4,5}NN Auger electrons from krypton partly overlap in energy with the 3d inner-shell photoelectrons and do not show these anomalous features. This Letter offers new insights into the inner-shell electron dynamics of heavy atoms in the giant dipole resonance region, laying the groundwork for attosecond soft x-ray spectroscopy of molecular systems containing iodine or bromine atoms.

Coulomb explosion imaging (CEI) is a powerful experimental technique that maps a molecule's geometric structure onto the momenta of ionic molecular fragments produced by rapid multiple ionization. Here, we apply CEI induced by pulses from an X-ray free-electron laser in order to image and distinguish complex hydrocarbon isomers with the chemical formula C7H8: toluene, cycloheptatriene, and 1,6-heptadiyne. The measured fragment-ion momentum distributions show discernible differences between the three isomers and provide signatures of specific carbon and hydrogen sites in the molecule. In contrast to previous work, we demonstrate that distinct 'marker atoms' are not strictly required for constructing a meaningful molecular frame of reference for the interpretation of the momentum-space data. Our work paves the way for tracking the ultrafast motion of nuclei during isomerization reactions in pure hydrocarbons.

In strong-field ionization of molecules, intense light pulses are thought to have a negligible direct influence on atomic nuclei. Molecular dissociation is thus expected to be determined by the geometrical configuration of the molecular ion at the ionization instant. Contrary to this picture, we observe a counterintuitive electron-proton angular correlation and the formation of proton vortices following strong-field ionization of H_{2} molecules by bicircularly polarized two-color laser fields. We explain this phenomenon by the pathway interference and localization of the residual H_{2}^{+} electron in different angular-momentum states formed in the tail of the driving laser pulse. We validate this interpretation by combining a quantum-mechanical numerical simulation of the field-driven coupled electronic-nuclear dynamics and a semiclassical-trajectory model for the phase accumulation of the laser-driven electronic-nuclear wave packet. Our joint experimental and theoretical study reveals a general picture of vortex electron localization which can be used for controlling molecular-bond breaking with circularly polarized laser fields.

We investigated the generation and control of fast photoelectrons (PEs) by exposing plasmonic nanoparticles (NPs) to short infrared (IR) laser pulses with peak intensities between 1012 and 3 × 1013 W/cm2. Our measured and numerically simulated PE momentum distributions demonstrate the extent to which PE yields and cutoff energies are controlled by the NP size, material, and laser peak intensity. For strong-field photoemission from spherical silver, gold, and platinum NPs with diameters between 10 and 100 nm our results confirm and surpass extremely high PEs cutoff energies, up to several hundred times the incident laser-pulse ponderomotive energy, found recently for gold nanospheres [Saydanzad et al., Nanophotonics 12, 1931 (2023)]. As reported previously for dielectric NPs [Rupp et al., J. Mod. Opt. 64, 995 (2017)], at higher intensities the cutoff energies we deduce from measured and simulated PE spectra tend to converge to a metal-independent limit. We expect these characteristics of light-induced electron emission from prototypical plasmonic metallic nanospheres to promote the understanding of the electronic dynamics in more complex plasmonic nanostructures and the design of nanoscale light-controlled plasmonic electron sources for photoelectronic devices of applied interest.

Determining the absolute configuration of gas-phase molecules in position-space has long been a fundamental challenge in molecular physics. While strong-field-induced Coulomb explosion imaging (CEI) has emerged as a powerful tool for probing molecular stereochemistry in momentum-space, reconstructing the original three-dimensional structure of polyatomic molecules remains a long-standing challenge due to the inherent complexity of multidimensional inversion. Here, we introduce a deep learning framework that bridges this gap by directly recovering position-space molecular structures from Coulomb explosion momentum patterns. Our approach combines CEI simulations with a neural network trained to establish the mapping between momentum-space Newton plots and real-space geometries. The trained model demonstrates high fidelity in reconstructing the structure of CHF_3 from experimental CEI data. This generalizable framework can not only be extended to other molecular systems but also opens avenues for time-resolved structural analysis of molecular dynamics.

Structure-sensitive methods based on femtosecond light or electron pulses are now making it possible to measure how molecular structures change during light-induced processes. Despite significant progress, high-fidelity imaging of nuclear positions remains a challenge even for relatively small molecular systems and, notably, regarding the positions of hydrogen atoms. As demonstrated in recent work, X-ray-induced Coulomb explosion imaging (CEI) may overcome this obstacle, as its sensitivity does not depend on the mass of the imaged atoms. The photoinduced ring opening of the heterocyclic molecule 2(5H)-thiophenone has attracted recent interest. Here, we show that CEI offers a powerful route to imaging the peripheral H atoms in this molecule and thus, more generally, to tracking detailed nuclear motions (e.g., isomerizations) in organic molecules on ultrafast time scales. Specifically, we record momentum-space Coulomb explosion images that report on the three-dimensional positioning of all nuclei within the molecule, for instance, distinguishing H atoms in C-H bonds that lie within or are directed out of the plane defined by the heavy atoms. The prospect of imaging peripheral H atoms to probe photochemical dynamics is explored by coupling ab initio molecular dynamics with classical Coulomb explosion simulations, thereby differentiating potential photoproduct isomers, including those whose structures primarily differ in the position of the hydrogens.

The photochemistry of heterocyclic molecules plays a decisive role for processes and applications like DNA photo-protection from UV damage and organic photocatalysis. The photochemical reactivity of heterocycles is determined by the redistribution of photoenergy into electronic and nuclear degrees of freedom, initially involving ultrafast internal conversion. Most heterocycles are planar in their ground state and internal conversion requires symmetry breaking. To lower the symmetry, the molecule must undergo an out-of-plane motion, which has not yet been observed directly. Here we show using the example of 2-thiouracil, how Coulomb explosion imaging can be utilized to extract comprehensive information on this molecular deformation, linking the extracted deplanarization of the molecular geometry to the previously studied temporal evolution of its electronic properties. Particularly, the protons of the exploded molecule are well-suited messengers carrying rich information on its geometry at distinct times after electronic excitation. We expect that our new analysis approach centered on these peripheral protons can be adapted as a general concept for future time-resolved studies of complex molecules in the gas phase.

We demonstrate a novel multi-modal approach combining momentum-resolved ion emission spectroscopy, X-ray photoelectron spectroscopy, and coherent diffraction imaging to investigate enhanced H3+ formation on nanoparticle surfaces. Using the SQS instrument at European XFEL, we simultaneously captured single-shot 3D ion momentum distributions and diffraction patterns from individual nanoparticles, allowing direct correlation between particle morphology and surface reaction dynamics. Our results reveal enhanced trihydrogen cation formation on water-decorated nanoparticle surfaces through X-ray induced ionization processes. The multi-modal detection scheme provides unprecedented insight into the spatiotemporal evolution of surface chemistry at the nanoscale.

Because of the Heisenberg uncertainty principle, the structure of a molecule fluctuates about its mean geometry, even in the ground state. Observing this fundamental quantum effect experimentally-particularly, revealing the collective nature of the structural quantum fluctuations-remains an unmet challenge for complex molecules. In this work, we achieved this for an 11-atom molecule by inducing its Coulomb explosion with an x-ray free-electron laser. We show that the structural fluctuations manifest themselves in correlated variations of ion momenta obtained through coincident detection of the atomic fragments from individual molecules. Our analysis scheme allows extracting these variations, despite our measurements covering only a fraction of the full 33-dimensional momentum space, thereby establishing a general approach for extracting information on high-dimensional structural dynamics using Coulomb explosion.

Light-induced molecular dynamics often involve the excitation of several electronic, vibrational, and rotational states. Since the ensuing electronic and nuclear motion determines the pathways and outcomes of photoinduced reactions, our ability to monitor and understand these dynamics is crucial for molecular physics, physical chemistry, and photobiology. However, characterizing this complex motion represents a significant challenge when different degrees of freedom are strongly coupled. In this Letter, we demonstrate how the interplay between vibrational, rotational, and electronic degrees of freedom governs the evolution of molecular wave packets in the low-lying states of strong-field-ionized sulfur dioxide. Using time-resolved Coulomb explosion imaging (CEI) and quantum mechanical wave packet simulations, we directly map the bending vibrations of the molecule, show how the vibrational wave packet is influenced by molecular alignment, and elucidate the consequences of nuclear motion for the coupling between the two lowest electronic states of the cation. Our results demonstrate that multi-coincident CEI can be an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.

Tracking the motion of individual atoms during chemical reactions represents a severe experimental challenge, especially if several competing reaction pathways exist or if the reaction is governed by the correlated motion of more than two molecular constituents. Here we demonstrate how ultrashort X-ray pulses combined with coincident ion imaging can be used to trace molecular iodine elimination from laser-irradiated diiodomethane (CH2I2), a reaction channel of fundamental importance but small relative yield that involves the breaking of two molecular bonds and the formation of a new one. We map bending vibrations of the bound molecule, disentangle different dissociation pathways, image the correlated motion of the iodine atoms and the methylene group leading to molecular iodine ejection, and trace the vibrational motion of the formed product. Our results provide a quantitative mechanistic picture behind previously suggested reaction mechanisms and prove that a variety of geometries are involved in the molecular bond formation.