Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in missing low-angle scattering data, which limits accurate real-space reconstruction. We develop an iterative algorithm to recover the missing low-angle signal in two-dimensional diffraction patterns. The method transforms between momentum-transfer and real-space domains using coupled Fourier and Abel transforms, while enforcing real-space support constraints to suppress reconstruction artifacts. Importantly, the algorithm requires only minimal a priori knowledge of the molecular structure, namely the approximate shortest and longest internuclear distances. We demonstrate accurate reconstruction of the missing signal using both simulated data and experimental diffraction patterns from laser-aligned trifluoroiodomethane (CF3I) molecules, enabling improved real-space structural retrieval from incomplete diffraction data. Our results remove a fundamental experimental limitation in ultrafast diffraction and establish a general route toward complete structural retrieval from incomplete scattering data.

Gas phase ultrafast electron diffraction (GUED) has become a powerful technique to directly observe the structural dynamics of photoexcited molecules. GUED reveals information about the nuclear motions that is complementary to the information on the electronic states provided by spectroscopic measurements. GUED experiments so far have utilized a single laser pulse to excite the molecules and an electron pulse to probe the dynamics. This limits the excited states that can be studied to only those that can be reached by absorption of a photon from the ground state or in some cases simultaneous absorption of multiple photons. A broader class of experiments and dynamics can be accessed using two time-delayed laser pulses to access unexplored regions of the potential energy surfaces. As a proof-of-principle experiment using a double excitation, we studied the photodissociation of trifluoroiodomethane molecules that are pre-excited with an infrared (800 nm) femtosecond laser pulse before photodissociation is triggered with an ultraviolet (266 nm) femtosecond laser pulse. We have observed significant differences in the dissociation dynamics, with pre-excitation resulting in a slower dissociation process. This capability can offer insights into the evolution of nuclear wave packets in regions of the excited potential energy surface that are inaccessible in single-photon excitation. We present a methodology to carry out the measurement, analyze, and interpret the data that could be applied to a broad class of experiments.

We report an iterative algorithm to retrieve accurate real space information from gas phase ultrafast diffraction measurements with missing data at low momentum transfer. The algorithm operates in a manner similar to phase retrieval algorithms which transform signals back and forth between the signal domain and the Fourier transform domain and apply constraints to retrieve the missing phase. Our algorithm retrieves missing data that is not accessible experimentally by applying a real-space constraint that requires only an approximate a-priori knowledge of the shortest and longest internuclear distances in the molecule. We demonstrate successful retrieval of the missing data in simulated data and in experimentally measured electron diffraction signals of photo-dissociated iodobenzene molecules.

The structural dynamics of metal carbonyls are central to processes ranging from catalysis to organometallic synthesis. Here we investigate the photodissociation of a prototypical transition metal carbonyl, Fe(CO)5, using mega-electron-volt ultrafast electron diffraction. By separately tracking structural evolution along the axial and equatorial directions, we provide an atomistic, angle-resolved view of the nuclear motions preceding CO dissociation and infer key features of the excited-state potential energy surface from the experimental observations. We further show that vibrational coupling before reaching the conical intersection facilitates the loss of a random carbonyl ligand via the Berry pseudorotation mechanism.

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.

Two-dimensional (2D) ferroelectric materials like NbOI_2 have garnered significant interest, yet their temporal response and synergetic interaction with light remain underexplored. Previous studies on the polarization of oxide ferroelectrics have relied on time-resolved optical second harmonic generation or ultrafast X-ray scattering. Here, we probe the laser-induced polarization dynamics of 2D NbOI_2 nanocrystals using ultrafast transmission electron diffraction and deflectometry. The deflection of the electron pulses is directly sensitive to the changes in the polarization, while the diffraction signal captures the structural evolution. Excited with a UV laser pulse, the polarization of NbOI_2 is initially suppressed for two picoseconds, then it recovers and overshoots, leading to a transiently enhanced polarization persisting for over 200 ps. This recovery coincides with coherent acoustic phonon generation, triggering a piezoresponse in the NbOI_2 nanocrystals. Our results offer a new method for sensing the ferroelectric order parameter in femtosecond time scales.

We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. The method can also be applied to the calculation of x-ray diffraction patterns.

We have studied the photodissociation of gas-phase bromocyclopropane by 200 nm wavelength ultraviolet radiation using ultrafast electron diffraction. Bromocyclopropane is a prototypical molecule in the study of organobromides, a class of molecules that have a significant impact on atmospheric ozone depletion through their photochemistry. Previous studies have revealed two possible reaction pathways for the photodissociation of bromine from bromocyclopropane; either the C-Br bond dissociates, leaving behind a cyclopropyl ring, or there is a concerted opening of the cyclopropyl ring along with the C-Br bond dissociation. In this work, both our experimental and simulation results indicate that the majority of the UV-photoexcited BCP molecules (88% ± 11% in the experiment) follow the first reaction pathway, in which the cyclopropyl ring remains closed after homolytic C-Br bond cleavage. This direct bond dissociation occurs within the experimental time resolution of 270 fs. In order to differentiate between the possible reaction end-products, both of which have diffraction signals dominated by the bromine atom, a new analysis method has been employed, which is more sensitive to the structure of the end-products.

Ultrafast scattering techniques such as ultrafast electron diffraction and ultrafast x-ray diffraction have been utilized to elucidate the structural dynamics, reaction intermediates, and final products in molecular reactions following photoexcitation. The time-dependent structures are typically not directly retrieved from the experimental data, but they rely on comparison with calculations. The genetic algorithm (GA), a global optimization strategy, can be used to retrieve the molecular structures directly from diffraction patterns without any theoretical input. However, the robustness of the GA with respect to real experimental conditions such as a limited momentum transfer range, noise, and artifacts has not been studied in detail. In this work, we characterize the performance of the GA with simulated data that mimic realistic experimental conditions. We have developed and implemented a variant of the GA specific to diffraction measurements which performs better in the presence of imperfect data compared to the standard implementation of the GA. We demonstrate this method with both synthetic data and experimental ultrafast electron diffraction data on the UV-induced photodissociation of trifluoroiodomethane (CF3I) molecules.

Conjugated cyclic organic molecules are common across many fields such as pharmaceuticals, are naturally occurring in biological systems, and are used in synthetic materials. One particular area of interest from a photochemical point of view is the formation of highly strained cyclic organics. We investigate the photoinduced reaction of cyclopentadiene, a five-membered organic ring molecule, which can form strained three and four carbon rings after photoexcitation with UV light, with the gas-phase ultrafast electron diffraction instrument at the SLAC MeV-UED facility. Electron diffraction offers a direct probe sensitive to the nuclear geometry during the reaction, allowing for the determination of the distribution of products formed following photoexcitation. We observe the simultaneous formation of the highly strained ring-closed bicyclo[2.1.0]pentene and vibrationally hot cyclopentadiene within the temporal resolution of the experiment and determine the relative yield of all reaction products. The experimental results are in good agreement with the predictions of trajectory simulations.

Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps towards understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species amongst the emerging reaction products. Here, we show that mega-electronvolt ultrafast electron diffraction in combination with ab initio molecular dynamics calculations offer a powerful route to determining time-resolved populations of the various isomeric products formed after UV (266 nm) excitation of the five-membered heterocyclic molecule 2(5H)-thiophenone. This strategy provides experimental validation of the predicted high (~50%) yield of an episulfide isomer containing a strained 3-membered ring within ~1 ps of photoexcitation and highlights the rapidity of interconversion between the rival highly vibrationally excited photoproducts in their ground electronic state.

The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2.

Quantum-mechanical simulation of laser-induced alignment of asymmetric-top molecules at high temperatures has been a challenge due to the high computational cost required to model a large number of initial states of the molecular ensemble. Here, we report a method to reduce the computational time and memory requirements by using the symmetries of coefficients in the rotational wave packet. For the case of nonadiabatic alignment of asymmetric-top molecules with a linearly polarized laser pulse, we have theoretically derived the symmetries in the coefficients of the rotational wave packet produced by the induced-dipole interaction. The symmetries allow us to simulate rotational dynamics at higher rotational temperatures than previously possible by reducing both the memory requirements and the computation time by a factor of 8. We demonstrate simulated results of the rotational dynamics of 4-fluorobenzotrifluoride at multiple temperatures up to 300 K.

For many chemical reactions, it remains notoriously difficult to predict and experimentally determine the rates and branching ratios between different reaction channels. This is particularly the case for reactions involving short-lived intermediates, whose observation requires ultrafast methods. The UV photochemistry of bromoform (CHBr3) is among the most intensely studied photoreactions. Yet, a detailed understanding of the chemical pathways leading to the production of atomic Br and molecular Br2 fragments has proven challenging. In particular, the role of isomerization and/or roaming and their competition with direct C-Br bond scission has been a matter of continued debate. Here, gas-phase ultrafast megaelectronvolt electron diffraction (MeV-UED) is used to directly study structural dynamics in bromoform after single 267 nm photon excitation with femtosecond temporal resolution. The results show unambiguously that isomerization contributes significantly to the early stages of the UV photochemistry of bromoform. In addition to direct C-Br bond breaking within <200 fs, formation of iso-CHBr3 (Br-CH-Br-Br) is observed on the same time scale and with an isomer lifetime of >1.1 ps. The branching ratio between direct dissociation and isomerization is determined to be 0.4 ± 0.2:0.6 ± 0.2, i.e., approximately 60% of molecules undergo isomerization within the first few hundred femtoseconds after UV excitation. The structure and time of formation of iso-CHBr3 compare favorably with the results of an ab initio molecular dynamics simulation. The lifetime and interatomic distances of the isomer are consistent with the involvement of a roaming reaction mechanism.

Advances in X-ray free electron lasers have made ultrafast scattering a powerful method for investigating molecular reaction kinetics and dynamics. Accurate measurement of the ground-state, static scattering signals of the reacting molecules is pivotal for these pump-probe X-ray scattering experiments as they are the cornerstone for interpreting the observed structural dynamics. This article presents a data calibration procedure, designed for gas-phase X-ray scattering experiments conducted at the Linac Coherent Light Source X-ray Free-Electron Laser at SLAC National Accelerator Laboratory, that makes it possible to derive a quantitative dependence of the scattering signal on the scattering vector. A self-calibration algorithm that optimizes the detector position without reference to a computed pattern is introduced. Angle-of-scattering corrections that account for several small experimental non-idealities are reported. Their implementation leads to near quantitative agreement with theoretical scattering patterns calculated with ab-initio methods as illustrated for two X-ray photon energies and several molecular test systems.

Conjugated diene molecules are highly reactive upon photoexcitation and can relax through multiple reaction channels that depend on the position of the double bonds and the degree of molecular rigidity. Understanding the photoinduced dynamics of these molecules is crucial for establishing general rules governing the relaxation and product formation. Here, we investigate the femtosecond time-resolved photoinduced excited-state structural dynamics of cis,cis-1,3-cyclooctadiene, a large-flexible cyclic conjugated diene molecule, upon excitation with 200 nm using mega-electron-volt ultrafast electron diffraction and trajectory surface hopping dynamics simulations. We tracked the photoinduced structural changes from the Franck-Condon region through the conical intersection seam to the ground state. Our findings revealed a novel primary reaction coordinate involving ring distortion, where the ring stretches along one axis and compresses along the perpendicular axis. The nuclear wavepacket remains compact along this reaction coordinate until it reaches the conical intersection seam, and it rapidly spreads as it approaches the ground state, where multiple products are formed.

The dynamics of cyclopentadiene (CP) following optical excitation at 243 nm was investigated by time-resolved pump-probe X-ray scattering using 16.2 keV X-rays at the Linac Coherent Light Source (LCLS). We present the first ultrafast structural evidence that the reaction leads directly to the formation of bicyclo[2.1.0]pentene (BP), a strained molecule with three- and four-membered rings. The bicyclic compound decays via a thermal backreaction to the vibrationally hot CP with a time constant of 21 ± 3 ps. A minor channel leads to ring-opened structures on a subpicosecond time scale.

As the simplest nitroaromatic compound, nitrobenzene is an interesting model system to explore the rich photochemistry of nitroaromatic compounds. Previous measurements of nitrobenzene's photochemical dynamics have probed structural and electronic properties, which, at times, paint a convoluted and sometimes contradictory description of the photochemical landscape. A sub-picosecond structural probe can complement previous electronic measurements and aid in determining the photochemical dynamics with less ambiguity. We investigate the ultrafast dynamics of nitrobenzene triggered by photoexcitation at 267 nm employing megaelectronvolt ultrafast electron diffraction with femtosecond time resolution. We measure the first 5 ps of dynamics and, by comparing our measured results to simulation, we unambiguously distinguish the lowest singlet and triplet electronic states. We observe ground state recovery within 160 +/- 60 fs through internal conversions and without signal corresponding to photofragmentation. Our lack of dissociation signal within the first 5 ps indicates that previously observed photofragmenation reactions take place in the vibrationally "hot" ground state on timescales considerably beyond 5 ps.