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Differentiating Three-Dimensional Molecular Structures Using Laser-Induced Coulomb Explosion Imaging

Coulomb explosion imaging (CEI) with x-ray free electron lasers has recently been shown to be a powerful method for obtaining detailed structural information of gas-phase planar ring molecules [R. Boll et al., X-ray multiphoton-induced Coulomb explosion images complex single molecules, Nat. Phys. 18, 423 (2022).]. In this Letter, we investigate the potential of CEI driven by a tabletop laser and extend this approach to differentiating three-dimensional structures. We study the static CEI patterns of planar and nonplanar organic molecules that resemble the structures of typical products formed in ring-opening reactions. Here, our results reveal that each molecule exhibits a well-localized and distinctive pattern in three-dimensional fragment-ion momentum space. We find that these patterns yield direct information about the molecular structures and can be qualitatively reproduced using a classical Coulomb explosion simulation. Our findings suggest that laser-induced CEI can serve as a robust method for differentiating molecular structures of organic ring and chain molecules. As such, it holds great promise as a method for following ultrafast structural changes, e.g., during ring-opening reactions, by tracking the motion of individual atoms in pump-probe experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

Visualizing the Three-Dimensional Arrangement of Hydrogen Atoms in Organic Molecules by Coulomb Explosion Imaging

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(5 H )-thiophenone has attracted recent interest. Here, in this work, 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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Generative modeling enables molecular structure retrieval from Coulomb explosion imaging

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 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 non-linear 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.

Artificial Intelligence (cs.AI)↗

Multiparticle cumulant mapping for Coulomb explosion imaging: Calculations and algorithm

We present a versatile cumulant mapping algorithm for analyzing correlated particle emission, offering insights into complex electronic and nuclear dynamics. Recently, we have demonstrated the use of cumulant mapping to extract information-rich correlations between the momenta of multiple fragments produced in Coulomb explosion imaging experiments [C. Cheng et al., Phys. Rev. Lett. 130, 093001 (2023)]. We define cumulant mapping in terms of histograms, enabling fast computation of linear (additive) observables. However, applying the same algorithm to nonlinear (nonadditive) observables poses challenges, as the computation time of conventional estimators scales nonlinearly with data size. To overcome this, we develop estimators and an accompanying algorithm to enable computationally efficient estimation of the cumulant of interest. Comparisons of computation times and signal-to-noise ratios reveal the superior performance of our approach. This method is demonstrated on the (D+, D+, C+, O+) dissociation channel of CD 2 ⁢O 4+ produced in a strong-field ionization experiment. Additionally, Poisson statistics are used to simulate the two methods and provide insights into the efficiency of our algorithm. The proposed methodology unlocks efficient computation of cumulant mapping for a broader range of complex systems and observables, such as the laser pulse dependence of ionization dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

Direct observation of ultrafast symmetry reduction during internal conversion of 2-thiouracil using Coulomb explosion imaging

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.

Chemical physics↗

Two-Dimensional Projected-Momentum Covariance Mapping for Coulomb Explosion Imaging

We introduce projected-momentum covariance mapping, an extension of recoil-frame covariance mapping for 2D ion imaging studies. By considering the two-dimensional projection of the ion momenta as recorded by the detector, one opens the door to a complex suite of analysis tools adapted from three-dimensional momentum imaging studies. This includes the use of different frames of reference to unravel the dynamics of fragmentation and the application of fragment momentum constraints to isolate specific fragmentation channels. The technique is demonstrated on data from a two-dimensional ion imaging study of the Coulomb explosion of the cis and trans isomers of 1,2-dichloroethene, following strong-field ionization by an intense near-infrared femtosecond laser pulse. Classical simulations are used to guide the interpretation of projected-momentum covariance maps. The results offer a detailed insight into the distinct Coulomb explosion dynamics for this pair of isomers and lay the groundwork for future time-resolved studies of photoisomerization dynamics in this molecular system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Imaging Three-Dimensional Molecular Structure and Dynamics with Multiparticle Covariance and Cumulant Coulomb Explosion Analysis

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. Furthermore, 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.

Imaging↗

Imaging transient molecular configurations in UV-excited diiodomethane

Femtosecond structural dynamics of diiodomethane (CH 2 I 2 ) triggered by ultraviolet (UV) photoabsorption at 290 and 330 nm are studied using time-resolved coincident Coulomb explosion imaging driven by a near-infrared probe pulse. Here, we map the dominant single-photon process, the cleavage of the carbon–iodine bond producing rotationally excited CH 2 I radical, identify the contributions of the three-body (CH 2 + I + I) dissociation and molecular iodine formation channels, which are primarily driven by the absorption of more than one UV photon, and demonstrate the existence of a weak reaction pathway involving the formation of short-lived transient species resembling iso-CH 2 I 2 -like geometries with a slightly shorter I–I separation compared to the ground-state CH 2 I 2 . These transient molecular configurations, which can be separated from the other channels by applying a set of conditions on the correlated momenta of three ionic fragments, are formed within ∼100 fs after the initial photoexcitation and decay within the next 100 fs.

Atomic and molecular processes↗

Simultaneous imaging of vibrational, rotational, and electronic wave-packet dynamics in a triatomic molecule

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. Furthermore, our results demonstrate that multicoincident CEI can be an efficient experimental tool for characterizing coupled electronic and nuclear motion in polyatomic molecules.

Atomic & molecular processes in external fields↗

Fragmentation dynamics of CS 2 dications and trications following S 2p ionization

Here, we present the results from a detailed study of the fragmentation dynamics of CS$_2^{2+}$ and CS$_2^{3+}$, 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 CS 2 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.

Allum, Felix [Deutsches Elektronen-Synchrotron (DE↗

Electron–Ion Covariance Reveals Geometry-Resolved Inner-Shell Spectra in CS 2 Photodissociation

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 CS 2 probed by ionization above the S 2p edge. Electron–ion covariance with time- and momentum-selected S + and S 2+ ions isolates distinct S 2p photoelectron spectra for ground-state CS 2 , bent photoexcited CS 2 , 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. Here, 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.

Ionization↗

Exploiting correlations in multi-coincidence Coulomb explosion patterns for differentiating molecular structures using machine learning

Coulomb explosion imaging (CEI) is a powerful technique for capturing the real-time motion of individual atoms during ultrafast photochemical reactions. CEI generates high-dimensional data with naturally embedded correlations that allow mapping the coordinated motion of nuclei in molecules. This enables reliable separation of competing reaction pathways and makes this approach uniquely suited for characterizing weak reaction channels. However, rich information contained in experimental CEI patterns remains largely underexploited due to challenges in visualizing correlations between multiple observables in multi-dimensional parameter space. Here we present a new approach to CEI of intermediate-sized polyatomic molecules, detecting up to eight ionic fragments in coincidence and leveraging machine-learning-based analysis to identify patterns and correlations in the resulting high-dimensional momentum-space data, enabling robust molecular structure identification and differentiation. Our approach provides high-dimensional background-free data encoding exceptionally rich structural information and establishes an automated, scalable framework for extracting insightful information from the data. As a demonstration, we apply this method to image and distinguish dichloroethylene isomers, showcasing its potential for broader applications in molecular imaging. Our results pave the way for channel-specific analysis of ultrafast structural dynamics in chemically relevant systems, particularly for disentangling mixed reaction pathways and detecting contributions from weak channels and minority species.

Chemical Physics (physics.chem-ph)↗

Distinguishing the XUV-induced Coulomb explosion dynamics of iodobenzene using covariance analysis

The primary and secondary fragmentation dynamics of iodobenzene following its ionization at 120 eV were determined using three-dimensional velocity map imaging and covariance analysis. Site-selective iodine 4d ionization was used to populate a range of excited polycationic parent states, which primarily broke apart at the carbon-iodine bond to produce I+ with phenyl or phenyl-like cations (C n H x + or C n H, with n = 1 – 6 and x = 1 – 5). The molecular products were produced with varying degrees of internal excitation and dehydrogenation, leading to stable and unstable outcomes. This further allowed the secondary dynamics of C 6 H x 2+ intermediates to be distinguished using native-frame covariance analysis, which isolated these processes in their own centre-of-mass reference frames. Furthermore, the mass resolution of the imaging mass spectrometer used for these measurements enabled the primary and secondary reaction channels to be specified at the level of individual hydrogen atoms, demonstrating the ability of covariance analysis to comprehensively measure the competing fragmentation channels of aryl cations, including those involving intermediate steps.

74 ATOMIC AND MOLECULAR PHYSICS↗

Visualizing the strong field–induced molecular breakup of C 60 via x-ray diffraction

Laser-driven dynamics in polyatomic molecules poses a complex many-body problem. Understanding intense light-matter interaction is crucial for steering intramolecular quantum dynamical processes. Here, we record time-resolved x-ray diffraction images of C 60 molecules during and after their interaction with intense near-infrared fields, giving direct access to structural changes of the molecules and their fragmentation in real time. Tuning the intensity of the excitation pulses, we uncover a transition from a weak-field regime of excited but stable molecules to a high-field regime dominated by Coulomb explosion. In the transition region, the molecules expand by up to 50% of their initial size within just 140 fs, with major fragmentation only setting in afterward. This work demonstrates that x-ray diffractive imaging is capable of retrieving time-resolved structural information of large molecules reshaped by intense laser fields. Laser-driven fragmentation is a first step toward observing molecular processes modified by laser fields of increasing intensity.

Schnorr, Kirsten [Paul Scherrer Inst. (PSI), Villi↗