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.

The inner-shell ionization of selenophene at 120 eV produces a rich array of fragmentation dynamics, including many originating from Auger-Meitner processes. In this report, three-dimensional velocity-map imaging and covariance analysis were used to identify and characterize over 50 distinct selenophene fragmentation channels. The majority resulted in two or three ‘heavy’ products containing selenium or carbon, many of which had identical mass-to-charge ratios but different chemical compositions due to the degree of hydrogenation and the selenium isotope involved. Covariance analysis was used to isolate these reaction channels and to provide estimates of their relative yields. In combination with prior similar studies on thiophene and furan, the current results indicate that the nature of the heteroatom significantly influences the charge redistribution and bond cleavage dynamics induced by the Auger-Meitner process, and demonstrate the sensitivity of inner-shell ionization dynamics to the molecular and electronic structures of heterocyclic systems.

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 chemical shifts of inner-shell atomic orbitals are highly sensitive to chemical bonding and molecular structure. In evolving systems, however, the spectra of distinct molecular species and geometries overlap, obscuring the underlying chemical dynamics. Here we demonstrate the use of electron-ion covariance analysis to combine the structural sensitivity of Coulomb explosion imaging with inner-shell spectroscopy, yielding geometry-specific spectra of transient and product species. We apply this approach to the excited state dynamics of CS2 probed by ionization above the S 2p edge. Electron-ion covariance with time- and momentum-selected S+ and S2+ ions isolates distinct S 2p photoelectron spectra for ground-state CS2, bent photoexcited CS2, the CS photoproduct, and bare atomic sulfur ─ species whose spectra overlap strongly in the channel-averaged measurement. Clear chemical shifts are observed in the covariance photoelectron spectrum for each of these species, all of which are consistent with high-level calculations. By extracting the atomic S contribution to the photoelectron spectrum in a finely time-resolved manner we can disentangle this contribution to the overall time-resolved photoelectron spectrum as the photodissociation proceeds. These results demonstrate the promise of electron-ion covariance as a general approach to geometry-resolved inner-shell spectroscopy, opening a route to tracking structural evolution through chemical shifts in complex photoexcited molecules.

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.

Time-resolved X-ray photoelectron spectroscopy (XPS) is used to track the photodissociation dynamics of 2-iodothiophene following 262 nm excitation. The transient XPS features include both direct ionization of the initially populated excited states and pronounced satellite peaks arising from shake-down processes. While the direct ionization signals exhibit only minimal energy shifts during C-I bond cleavage, the shake-down transitions undergo a substantial, 5 eV, shift over the reaction coordinate. By correlating these shifts with simulated C-I bond lengths, a direct structural mapping is established that reveals the exceptional sensitivity of shake-down channels to molecular geometry. These results demonstrate that shake-down transitions provide a new and powerful probe of ultrafast structural dynamics.

Using intense femtosecond soft x-ray pulses above the sulfur 2p edge produced by the Free-electron LASer in Hamburg (FLASH), we investigate the multiple ionization and fragmentation dynamics of CS2. We focus on the three-ion fragmentation pathways of CS2 polycations with total charges of +4 to +10, which can only be reached through absorption of multiple x-ray photons. By coupling three-dimensional velocity map imaging with covariance analysis, we determine the relative momentum distribution of all ions produced in each fragmentation channel at high ion count rates per shot. Deviations between these measured relative ion momentum distributions and those predicted by classical Coulomb explosion simulations, assuming an instantaneous charge buildup, grow with increasing total charge state, indicative of nuclear motion during the multiple ionizations that occur within the x-ray pulse duration-as confirmed by comparison with the main fragmentation channel of the trication, which can be formed following single-photon interaction. These dynamics can be modeled using a gradual charge buildup picture of sequential single-photon single-ionization events occurring during the pulse, following the initial core ionization. Our study underscores the importance of complete and channel-resolved measurements, the advances enabled by covariance analysis in high-count-rate experiments, and the critical role of charge buildup and nuclear dynamics during the x-ray free-electron laser pulse in Coulomb explosion imaging. The impacts of this nuclear motion can be controlled and minimized by utilizing shorter x-ray pulses, as will be of great importance in using time-resolved x-ray Coulomb explosion to probe the fastest dynamics in molecular photochemistry.

Coulomb explosion imaging (CEI) provides a direct means of imaging molecular geometry by correlating fragment ion momenta following the fragmentation of a molecular polycation. Here, we demonstrate the use of three-body covariance and four-body cumulant analysis to extract three-dimensional (3D) structural information from the X-ray-induced Coulomb explosion of tert-butyl iodide (C4H9I). Site-selective ionization at the iodine 4d edge with intense femtosecond soft X-ray pulses from an X-ray free-electron laser (XFEL) enables rapid charge buildup and molecular breakup. By correlating ionic fragments in the molecular frame, we isolate complete dissociation channels and reveal subtle structural changes, such as umbrella-type motion of the branched alkyl chain, during the ionization process. Comparison with point-charge simulations of the Coulomb explosion shows close agreement, validating the approach. These results establish covariance/cumulant mapping as a powerful strategy for imaging complex three-dimensional molecular structures and point the way toward time-resolved CEI using both XFEL and tabletop sources for capturing ultrafast structural dynamics.

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.

We present the results from a detailed study of the fragmentation dynamics of CS22+ and CS23+, formed in intense femtosecond soft x-ray pulses above the sulfur 2p edge, primarily through single core photoionization from the S 2p site, and subsequent Auger-Meitner decay(s). By combining three-dimensional velocity map imaging with covariance analysis, we determine the relative momenta of the ions produced in each two- and three-body fragmentation channel, at significantly higher ion count rates than conventional coincidence measurements. We shed new light on the wide range of fragmentation channels observed from the CS2 dication and trication, including channels that involve ionization-induced bond formation and fragmentations producing undetected neutral cofragments. In the latter case, a "native frames" approach is used to isolate contributions from concerted and sequential fragmentations and extract dynamical information about each step of a concerted fragmentation process. While dications often fragment sequentially, the trication is dominated by concerted fragmentation. The main trication fragmentation channel into S+ + C+ + S+ can be well-approximated by classical Coulombic simulations of the ground-state geometry distribution, reflecting both the nature of the trication potential energy surface and the rapid multiple ionization prior to substantial structural dynamics. This study demonstrates ways in which fundamental insights into the fragmentation dynamics of polycations following x-ray ionization may be extracted, which will be beneficial to future studies that employ time-resolved x-ray Coulomb explosion imaging to study ultrafast photochemistry.

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.

Ultrashort XUV pulses of the Free-Electron-LASer in Hamburg (FLASH) were used to investigate laser-induced fragmentation patterns of the prototypical chiral molecule 1-iodo-2-methyl-butane (C_5H_11I) in a pump-probe scheme. Ion velocity-map images and mass spectra of optical-laser-induced fragmentation were obtained for subsequent FEL exposure with photon energies of 63 eV and 75 eV. These energies specifically address the iodine 4d edge of neutral and singly charged iodine, respectively. The presented ion spectra for two optical pump-laser wavelengths, i.e., 800 nm and 267 nm, reveal substantially different cationic fragment yields in dependence on the wavelength and intensity. For the case of 800-nm-initiated fragmentation, the molecule dissociates notably slower than for the 267-nm pump. The results underscore the importance of considering optical-laser wavelength and intensity in the dissociation dynamics of this prototypical chiral molecule that is a promising candidate for future studies of its asymmetric nature.

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.

Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, which provide insight into the local environment, traditionally require different approaches and are often studied separately. Here, we demonstrate that X-ray pulses from a seeded free-electron laser (FEL) enable the measurement of high-resolution, time-resolved X-ray photoelectron spectra (XPS) that capture weak satellite states resulting from shake-down processes in a valence-excited molecule. This approach effectively combines the advantages of both valence- and core-state investigations. We applied this method to investigate photoexcited CS_2 molecules, where the role of internal conversion (IC) and intersystem crossing (ISC) in determining the pre-dissociation dynamics is controversial. We present XPS spectra from photoexcited CS_2, obtained at the FERMI FEL. High-resolution measurements, compared to the corresponding spectra obtained from accurate multireference quantum chemical calculations, reveal that shake-down satellite channels are highly sensitive to both valence electronic and geometric changes. Previous studies of the pre-dissociation dynamics have led to uncertain assignments of the branching between singlet and triplet excited states. We derive a propensity rule that demonstrates the spin-selectivity of the shake-downs. This selectivity allows us to unequivocally assign contributions from the bright and dark singlet excited states, with populations tracked along the pre-dissociation dynamic pathway.

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.