Imaging CF3I conical intersection and photodissociation dynamics with ultrafast electron diffraction

The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase ultrafast electron diffraction (UED) technique has attracted significant attention as a unique tool for monitoring photochemical and photophysical processes at the all-atomic level with high temporal and spatial resolutions. In this work, we simulate the UED spectra of cyclobutanone using the trajectory surface hopping method at the extended multi-state complete active space second order perturbation theory (XMS-CASPT2) level and thereby predict the results of the upcoming UED experiments in the Stanford Linear Accelerator Laboratory. The simulated results demonstrate that a few pathways, including the C2 and C3 dissociation channels, as well as the ring opening channel, play important roles in the nonadiabatic reactions of cyclobutanone. We demonstrate that the simulated UED signal can be directly interpreted in terms of atomic motions, which provides a unique way of monitoring the evolution of the molecular structure in real time. Our work not only provides numerical data that help to determine the accuracy of the well-known surface hopping dynamics at the high XMS-CASPT2 electronic-structure level but also facilitates the understanding of the microscopic mechanisms of the photoinduced reactions in cyclobutanone.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

Photo-induced structural dynamics of o-nitrophenol by ultrafast electron diffraction

The photo-induced dynamics of o-nitrophenol, particularly its photolysis, has garnered significant scientific interest as a potential source of nitrous acid in the atmosphere. Although the photolysis products and preceding photo-induced electronic structure dynamics have been investigated extensively, the nuclear dynamics accompanying the non-radiative relaxation of o-nitrophenol on the ultrafast timescale, which include an intramolecular proton transfer step, have not been experimentally resolved. Herein, we present a direct observation of the ultrafast nuclear motions mediating photo-relaxation using ultrafast electron diffraction. This work spatiotemporally resolves the loss of planarity which enables access to a conical intersection between the first excited state and the ground state after the proton transfer step, on the femtosecond timescale and with sub-Angstrom resolution. Our observations, supported by ab initio multiple spawning simulations, provide new insights into the proton transfer mediated relaxation mechanism in o-nitrophenol.

A comparative review of time-resolved x-ray and electron scattering to probe structural dynamics

The structure of molecules, particularly the dynamic changes in structure, plays an essential role in understanding physical and chemical phenomena. Time-resolved (TR) scattering techniques serve as crucial experimental tools for studying structural dynamics, offering direct sensitivity to molecular structures through scattering signals. Over the past decade, the advent of x-ray free-electron lasers (XFELs) and mega-electron-volt ultrafast electron diffraction (MeV-UED) facilities has ushered TR scattering experiments into a new era, garnering significant attention. In this review, we delve into the basic principles of TR scattering experiments, especially focusing on those that employ x-rays and electrons. We highlight the variations in experimental conditions when employing x-rays vs electrons and discuss their complementarity. Additionally, cutting-edge XFELs and MeV-UED facilities for TR x-ray and electron scattering experiments and the experiments performed at those facilities are reviewed. As new facilities are constructed and existing ones undergo upgrades, the landscape for TR x-ray and electron scattering experiments is poised for further expansion. Through this review, we aim to facilitate the effective utilization of these emerging opportunities, assisting researchers in delving deeper into the intricate dynamics of molecular structures.

Ultrafast photochemistry and electron-diffraction spectra in n → (3s) Rydberg excited cyclobutanone resolved at the multireference perturbative level

We study the ultrafast time evolution of cyclobutanone excited to the singlet n → Rydberg state through non-adiabatic surface-hopping simulationsperformed at extended multi-state complete active space second-order perturbation (XMS-CASPT2) level of theory. These dynamics predict relaxation to the ground-state with a timescale of 822 ± 45 fs with minimal involvement of the triplets. The major relaxation path to the ground-state involves a three-state degeneracy region and leads to a variety of fragmented photoproducts. We simulate the resulting time-resolved electron-diffraction spectra, which track the relaxation of the excited state and the formation of various photoproducts in the ground state.

Structure and Ultrafast X-ray Diffraction of the Hydrated Metaphosphate

We study the pathway of metaphosphate hydration when a metaphosphate anion is dissolved in liquid water with an explicit water model. For this purpose, we propose a sequential Monte Carlo algorithm incorporated with the ab initio quantum mechanics/molecular mechanics (QM/MM) method, which can reduce the amount of ab initio QM/MM sampling while retaining the accuracy of the simulation. We demonstrate the numerical calculation of the standard enthalpy change for the successive addition reaction PO3-·2H2O + H2O ⇌ PO3-·3H2O in the liquid phase, which helps to clarify the hydration pathway of the metaphosphate. With the obtained hydrated structure of the metaphosphate anion, we perform ab initio calculations for its relaxation dynamics upon vibrational excitation and characterize the energy transfer process in solution with simulated ultrafast X-ray diffraction signals, which can be experimentally implemented with X-ray free-electron lasers.

Predicting the photodynamics of cyclobutanone triggered by a laser pulse at 200 nm and its MeV-UED signals-A trajectory surface hopping and XMS-CASPT2 perspective

This work is part of a prediction challenge that invited theoretical/computational chemists to predict the photochemistry of cyclobutanone in the gas phase, excited at 200 nm by a laser pulse, and the expected signal that will be recorded during a time-resolved megaelectronvolt ultrafast electron diffraction (MeV-UED). We present here our theoretical predictions based on a combination of trajectory surface hopping with XMS-CASPT2 (for the nonadiabatic molecular dynamics) and Born-Oppenheimer molecular dynamics with MP2 (for the athermal ground-state dynamics following internal conversion), coined (NA+BO)MD. The initial conditions were sampled from Born-Oppenheimer molecular dynamics coupled to a quantum thermostat. Our simulations indicate that the main photoproducts after 2 ps of dynamics are CO + cyclopropane (50%), CO + propene (10%), and ethene and ketene (34%). The photoexcited cyclobutanone in its second excited electronic state S2 can follow two pathways for its nonradiative decay: (i) a ring-opening in S2 and a subsequent rapid decay to the ground electronic state, where the photoproducts are formed, or (ii) a transfer through a closed-ring conical intersection to S1, where cyclobutanone ring opens and then funnels to the ground state. Lifetimes for the photoproduct and electronic populations were determined. We calculated a stationary MeV-UED signal [difference pair distribution function-ΔPDF(r)] for each (interpolated) pathway as well as a time-resolved signal [ΔPDF(r,t) and ΔI/I(s,t)] for the full swarm of (NA+BO)MD trajectories. Furthermore, our analysis provides time-independent basis functions that can be used to fit the time-dependent experimental UED signals [both ΔPDF(r,t) and ΔI/I(s,t)] and potentially recover the population of photoproducts. We also offer a detailed analysis of the limitations of our model and their potential impact on the predicted experimental signals.

Electron scattering beyond the independent atom model: Quantum fluctuation of the Coulomb potential

In the past century, electron scattering has mostly served as a powerful tool to measure the microscopic structure of gases, liquids, and solids in either a static or time-resolved manner. One common basis for these works is the independent atom model, which directly relates electron scattering signals to the atomic structure of matter. In this perspective, we explore the information content of electron scattering that goes beyond the independent atom model. We show that the small-angle limit of the electron scattering signal encodes the quantum mechanical fluctuation of the long-range Coulomb potential. This quantum fluctuation, described by the second moment of the dipole operator, is the root cause of the intermolecular van der Waals forces.

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

Coherent x-ray spontaneous emission spectroscopy of conical intersections

Conical intersections are known to play a vital role in many photochemical processes. The breakdown of the Born-Oppenheimer approximation in the vicinity of a conical intersection causes exciting phenomena, such as the ultrafast radiationless decay of excited states. The passage of a molecule through a conical intersection creates a coherent superposition of electronic states via nonadiabatic couplings. Detecting this coherent superposition may serve as a direct probe of the conical intersection. In this paper, we theoretically demonstrate the use of coherent spontaneous emission in samples with long-range order for probing the occurrence of a conical intersection in a molecule. Our simulations show that the spectrum contains clear signatures of the created coherent superposition of electronic states. We investigate the bandwidth requirements for the x-ray probes, which influence the observation of coherent superposition generated by the conical intersection.

High energy electron diffraction instrument with tunable camera length

Ultrafast electron diffraction (UED) stands as a powerful technique for real-time observation of structural dynamics at the atomic level. In recent years, the use of MeV electrons from radio frequency guns has been widely adopted to take advantage of the relativistic suppression of the space charge effects that otherwise limit the temporal resolution of the technique. Nevertheless, there is not a clear choice for the optimal energy for a UED instrument. Scaling to beam energies higher than a few MeV does pose significant technical challenges, mainly related to the inherent increase in diffraction camera length associated with the smaller Bragg angles. In this study, we report a solution by using a compact post-sample magnetic optical system to magnify the diffraction pattern from a crystal Au sample illuminated by an 8.2 MeV electron beam. Our method employs, as one of the lenses of the optical system, a triplet of compact, high field gradients (>500 T/m), small-gap (3.5 mm) Halbach permanent magnet quadrupoles. Shifting the relative position of the quadrupoles, we demonstrate tuning the magnification by more than a factor of two, a 6× improvement in camera length, and reciprocal space resolution better than 0.1 Å-1 in agreement with beam transport simulations.

Time-resolved x-ray spectroscopy of nucleobases and their thionated analogs

The photoinduced relaxation dynamics of nucleobases and their thionated analogs have been investigated extensively over the past decades motivated by their crucial role in organisms and their application in medical and biochemical research and treatment. Most of these studies focused on the spectroscopy of valence electrons and fragmentation. The advent of ultrashort x-ray laser sources such as free-electron lasers, however, opens new opportunities for studying the ultrafast molecular relaxation dynamics utilizing the site- and element-selectivity of x-rays. In this review, we want to summarize ultrafast experiments on thymine and 2-thiouracil performed at free-electron lasers. We performed time-resolved x-ray absorption spectroscopy at the oxygen K-edge after UV excitation of thymine. In addition, we investigated the excited state dynamics of 2-tUra via x-ray photoelectron spectroscopy at sulfur. For these methods, we show a strong sensitivity to the electronic state or charge distribution, respectively. We also performed time-resolved Auger-Meitner spectroscopy, which shows spectral shifts associated with internuclear distances close to the probed site. We discuss the complementary aspects of time-resolved x-ray spectroscopy techniques compared to optical and UV spectroscopy for the investigation of ultrafast relaxation processes.

Monitoring the Evolution of Relative Product Populations at Early Times during a Photochemical Reaction

Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps toward understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species among 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 three-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.

A Complete Unveiling of the Mechanism and Chirality in Photoisomerization of Arylazopyrazole 3pzH: Combined Electronic Structure Calculations and AIMS Dynamic Simulations

The arylazopyrazole 3pzH as a novel photoswitch exhibits quantitative switching and high thermal stability. In this work, combined electronic structure calculations and ab initio multiple spawning (AIMS) dynamic simulations were performed to systemically investigate the cis ↔ trans photoisomerization mechanism and the chiral preference after photoexcitation of 3pzH to the first excited singlet state (S1). Unlike most of the azoheteroarene photoswitches reported previously, many twisted and T-shaped cis isomers were found to be stable for 3pzH in the S0 state, owing to the moderate interaction between the hydrogen atom and π electrons of the aromatic ring. Two twisted cis isomers with different chirality ((M)-Z1 and (P)-Z1), the most stable T-shaped cis isomer ((T)-Z2), and the most stable planar trans isomer (E2) were selected as the initial structures to carry out the AIMS nonadiabatic dynamic simulations. Following excitation to the S1 state, all of the cis isomers decayed to conical intersection (CI) regions via the same bicycle pedal mechanism, while the evolution of the trans isomers to their CI regions was achieved via rotation around the N═N bond. More importantly, chiral preferences were found for the twisted cis isomers in the S1 state through the AIMS dynamic simulations due to the steric effect and static electronic repulsion. Notably, chirality was also observed in S1 isomerization starting from the planar E2 isomer because of the dynamic effect. After the nonadiabatic transition to the S0 state, the bicycle pedal mechanism was found to play a crucial role in cis ↔ trans photoisomerization. The simulated photoisomerization productivities were generally consistent with past experimental observations. Our calculations not only uncover the underlying reason for the excellent photoswitching properties of 3pzH but also enrich the knowledge of photoisomerization for azoheteroarene photoswitches, which will surely benefit their rational design.

Unraveling the ultrafast dynamics of thermal-energy chemical reactions

In this perspective, we discuss how one can initiate, image, and disentangle the ultrafast elementary steps of thermal-energy chemical dynamics, building upon advances in technology and scientific insight. We propose that combinations of ultrashort mid-infrared laser pulses, controlled molecular species in the gas phase, and forefront imaging techniques allow to unravel the elementary steps of general-chemistry reaction processes in real time. We detail, for prototypical first reaction systems, experimental methods enabling these investigations, how to sufficiently prepare and promote gas-phase samples to thermal-energy reactive states with contemporary ultrashort mid-infrared laser systems, and how to image the initiated ultrafast chemical dynamics. The results of such experiments will clearly further our understanding of general-chemistry reaction dynamics.

Capturing the generation and structural transformations of molecular ions

Molecular ions are ubiquitous and play pivotal roles1-3 in many reactions, particularly in the context of atmospheric and interstellar chemistry4-6. However, their structures and conformational transitions7,8, particularly in the gas phase, are less explored than those of neutral molecules owing to experimental difficulties. A case in point is the halonium ions9-11, whose highly reactive nature and ring strain make them short-lived intermediates that are readily attacked even by weak nucleophiles and thus challenging to isolate or capture before they undergo further reaction. Here we show that mega-electronvolt ultrafast electron diffraction (MeV-UED)12-14, used in conjunction with resonance-enhanced multiphoton ionization, can monitor the formation of 1,3-dibromopropane (DBP) cations and their subsequent structural dynamics forming a halonium ion. We find that the DBP+ cation remains for a substantial duration of 3.6 ps in aptly named 'dark states' that are structurally indistinguishable from the DBP electronic ground state. The structural data, supported by surface-hopping simulations15 and ab initio calculations16, reveal that the cation subsequently decays to iso-DBP+, an unusual intermediate with a four-membered ring containing a loosely bound17,18 bromine atom, and eventually loses the bromine atom and forms a bromonium ion with a three-membered-ring structure19. We anticipate that the approach used here can also be applied to examine the structural dynamics of other molecular ions and thereby deepen our understanding of ion chemistry.

Relativistic ultrafast electron diffraction at high repetition rates

The ability to resolve the dynamics of matter on its native temporal and spatial scales constitutes a key challenge and convergent theme across chemistry, biology, and materials science. The last couple of decades have witnessed ultrafast electron diffraction (UED) emerge as one of the forefront techniques with the sensitivity to resolve atomic motions. Increasingly sophisticated UED instruments are being developed that are aimed at increasing the beam brightness in order to observe structural signatures, but so far they have been limited to low average current beams. Here, we present the technical design and capabilities of the HiRES (High Repetition-rate Electron Scattering) instrument, which blends relativistic electrons and high repetition rates to achieve orders of magnitude improvement in average beam current compared to the existing state-of-the-art instruments. The setup utilizes a novel electron source to deliver femtosecond duration electron pulses at up to MHz repetition rates for UED experiments. Instrument response function of sub-500 fs is demonstrated with < 100 fs time resolution targeted in future. We provide example cases of diffraction measurements on solid-state and gas-phase samples, including both micro- and nanodiffraction (featuring 100 nm beam size) modes, which showcase the potential of the instrument for novel UED experiments.

Femtosecond Electronic and Hydrogen Structural Dynamics in Ammonia Imaged with Ultrafast Electron Diffraction

Directly imaging structural dynamics involving hydrogen atoms by ultrafast diffraction methods is complicated by their low scattering cross sections. Here we demonstrate that megaelectronvolt ultrafast electron diffraction is sufficiently sensitive to follow hydrogen dynamics in isolated molecules. In a study of the photodissociation of gas phase ammonia, we simultaneously observe signatures of the nuclear and corresponding electronic structure changes resulting from the dissociation dynamics in the time-dependent diffraction. Both assignments are confirmed by ab initio simulations of the photochemical dynamics and the resulting diffraction observable. While the temporal resolution of the experiment is insufficient to resolve the dissociation in time, our results represent an important step towards the observation of proton dynamics in real space and time.

Rehybridization dynamics into the pericyclic minimum of an electrocyclic reaction imaged in real-time

Electrocyclic reactions are characterized by the concerted formation and cleavage of both σ and π bonds through a cyclic structure. This structure is known as a pericyclic transition state for thermal reactions and a pericyclic minimum in the excited state for photochemical reactions. However, the structure of the pericyclic geometry has yet to be observed experimentally. We use a combination of ultrafast electron diffraction and excited state wavepacket simulations to image structural dynamics through the pericyclic minimum of a photochemical electrocyclic ring-opening reaction in the molecule α-terpinene. The structural motion into the pericyclic minimum is dominated by rehybridization of two carbon atoms, which is required for the transformation from two to three conjugated π bonds. The σ bond dissociation largely happens after internal conversion from the pericyclic minimum to the electronic ground state. These findings may be transferrable to electrocyclic reactions in general.

Filming enhanced ionization in an ultrafast triatomic slingshot

Filming atomic motion within molecules is an active pursuit of molecular physics and quantum chemistry. A promising method is laser-induced Coulomb Explosion Imaging (CEI) where a laser pulse rapidly ionizes many electrons from a molecule, causing the remaining ions to undergo Coulomb repulsion. The ion momenta are used to reconstruct the molecular geometry which is tracked over time (i.e., filmed) by ionizing at an adjustable delay with respect to the start of interatomic motion. Results are distorted, however, by ultrafast motion during the ionizing pulse. We studied this effect in water and filmed the rapid "slingshot" motion that enhances ionization and distorts CEI results. Our investigation uncovered both the geometry and mechanism of the enhancement which may inform CEI experiments in many other polyatomic molecules.

Ultrafast X-Ray Probes of Elementary Molecular Events

Elementary events that determine photochemical outcomes and molecular functionalities happen on the femtosecond and subfemtosecond timescales. Among the most ubiquitous events are the nonadiabatic dynamics taking place at conical intersections. These facilitate ultrafast, nonradiative transitions between electronic states in molecules that can outcompete slower relaxation mechanisms such as fluorescence. The rise of ultrafast X-ray sources, which provide intense light pulses with ever-shorter durations and larger observation bandwidths, has fundamentally revolutionized our spectroscopic capabilities to detect conical intersections. Recent theoretical studies have demonstrated an entirely new signature emerging once a molecule traverses a conical intersection, giving detailed insights into the coupled nuclear and electronic motions that underlie, facilitate, and ultimately determine the ultrafast molecular dynamics. Following a summary of current sources and experiments, we survey these techniques and provide a unified overview of their capabilities. We discuss their potential to dramatically increase our understanding of ultrafast photochemistry.

A Nitrogen Out-of-Plane (NOOP) Mechanism for Imine-Based Light-Driven Molecular Motors

Light-driven molecular motors have generated considerable interest due to their potential applications in material and biological systems. Recently, Greb and Lehn reported a new class of molecular motors, chiral N-alkyl imines, which undergo unidirectional rotation induced by light and heat. The mechanism of unidirectional motion in molecular motors containing a C═N group has been assumed to consist of photoinduced torsion about the double bond. In this work, we present a computational study of the photoisomerization dynamics of a chiral N-alkyl imine motor. We find that the location and energetics of minimal energy conical intersections (MECIs) alone are insufficient to understand the mechanism of the motor. Furthermore, a key part of the mechanism consists of out-of-plane distortions of the N atom (followed by isomerization about the double bond). Dynamic effects and out-of-plane distortions are critical to understand the observed (rather low) quantum yield for photoisomerization. Our results provide hints as to how the photoisomerization quantum yield might be increased, improving the efficiency of this class of molecular motors.

Monitoring vibronic coherences and molecular aromaticity in photoexcited cyclooctatetraene with an X-ray probe: a simulation study

Understanding conical intersection (CI) dynamics and subsequent conformational changes is key for exploring and controlling photo-reactions in aromatic molecules. Monitoring of their time-resolved dynamics remains a formidable experimental challenge. In this study, we simulate the photoinduced S₃ to S₁ non-adiabatic dynamics of cyclooctatetraene (COT), involving multiple CIs with relaxation times in good agreement with experiment. We further investigate the possibility to directly probe the CI passages in COT by off-resonant X-ray Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). We find that these signals sensitively monitor key chemical features during the ultrafast dynamics. First, we distinguish two CIs by using TRUECARS signals with their appearances at different Raman shifts. Second, we demonstrate that TRXD, where X-ray photons scatter off electron densities, can resolve ultrafast changes in the aromaticity of COT. It can further distinguish between planar and non-planar geometries explored during the dynamics, as e.g. two different tetraradical-type CIs. The knowledge gained from these measurements can give unique insight into fundamental chemical properties that dynamically change during non-adiabatic passages.

Quantum Chaos in the Dynamics of Molecules

Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.

Ultrafast light-induced dynamics in the microsolvated biomolecular indole chromophore with water

Interactions between proteins and their solvent environment can be studied in a bottom-up approach using hydrogen-bonded chromophore-solvent clusters. The ultrafast dynamics following UV-light-induced electronic excitation of the chromophores, potential radiation damage, and their dependence on solvation are important open questions. The microsolvation effect is challenging to study due to the inherent mix of the produced gas-phase aggregates. We use the electrostatic deflector to spatially separate different molecular species in combination with pump-probe velocity-map-imaging experiments. We demonstrate that this powerful experimental approach reveals intimate details of the UV-induced dynamics in the near-UV-absorbing prototypical biomolecular indole-water system. We determine the time-dependent appearance of the different reaction products and disentangle the occurring ultrafast processes. This approach ensures that the reactants are well-known and that detailed characteristics of the specific reaction products are accessible - paving the way for the complete chemical-reactivity experiment.

Time-resolved X-ray and XUV based spectroscopic methods for nonadiabatic processes in photochemistry

The photochemistry of numerous molecular systems is influenced by conical intersections (CIs). These omnipresent nonadiabatic phenomena provide ultra-fast radiationless relaxation channels by creating degeneracies between electronic states and decide over the final photoproducts. In their presence, the Born-Oppenheimer approximation breaks down, and the timescales of the electron and nuclear dynamics become comparable. Due to the ultra-fast dynamics and the complex interplay between nuclear and electronic degrees of freedom, the direct experimental observation of nonadiabatic processes close to CIs remains challenging. In this article, we give a theoretical perspective on novel spectroscopic techniques capable of observing clear signatures of CIs. We discuss methods that are based on ultra-short laser pulses in the extreme ultraviolet and X-ray regime, as their spectral and temporal resolution allow for resolving the ultra-fast dynamics near CIs.

Electron-induced dissociation dynamics studied using covariance-map imaging

Recently, covariance analysis has found significant use in the field of chemical reaction dynamics. When coupled with data from product time-of-flight mass spectrometry and/or multi-mass velocity-map imaging, it allows us to uncover correlations between two or more ions formed from the same parent molecule. While the approach has parallels with coincidence measurements, covariance analysis allows experiments to be performed at much higher count rates than traditional coincidence methods. We report results from electron-molecule crossed-beam experiments, in which covariance analysis is used to elucidate the dissociation dynamics of multiply-charged ions formed by electron ionisation over the energy range from 50 to 300 eV. The approach is able to isolate signal contributions from multiply charged ions even against a very large 'background' of signal arising from dissociation of singly-charged parent ions. Covariance between the product time-of-flight spectra identifies pairs of fragments arising from the same parent ions, while covariances between the velocity-map images ('recoil-frame covariances') reveal the relative velocity distributions of the ion pairs. We show that recoil-frame covariance analysis can be used to distinguish between multiple plausible dissociation mechanisms, including multi-step processes, and that the approach becomes particularly powerful when investigating the fragmentation dynamics of larger molecules with a higher number of possible fragmentation pathways.

Photoinduced Ultrafast Transition of the Local Correlated Structure in Chalcogenide Phase-Change Materials

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge_{2}Sb_{2}Te_{5} has been widely used in optical data storage and nonvolatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation, and time-dependent density-functional theory molecular dynamic simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5}. The randomly oriented Peierls distortion among unit cells in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5} is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in the individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ∼0.3  ps. In addition, the impact of the carrier relaxation and the large number of vacancies to the ultrafast structural response is quantified and discussed. Our Letter provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Nonadiabatic Excited State Dynamics of Organic Chromophores: Take-Home Messages

Nonadiabatic excited state dynamics are important in a variety of processes. Theoretical and experimental developments have allowed for a great progress in this area, while combining the two is often necessary and the best approach to obtain insight into the photophysical behavior of molecules. In this Feature Article we use examples of our recent work combining time-resolved photoelectron spectroscopy with theoretical nonadiabatic dynamics to highlight important lessons we learned. We compare the nonadiabatic excited state dynamics of three different organic molecules with the aim of elucidating connections between structure and dynamics. Calculations and measurements are compared for uracil, 1,3-cyclooctadiene, and 1,3-cyclohexadiene. The comparison highlights the role of rigidity in influencing the dynamics and the difficulty of capturing the dynamics accurately with calculations.

Direct Monitoring of Conical Intersection Passage via Electronic Coherences in Twisted X-Ray Diffraction

Quantum coherences in electronic motions play a critical role in determining the pathways and outcomes of virtually all photophysical and photochemical molecular processes. However, the direct observation of electronic coherences in the vicinity of conical intersections remains a formidable challenge. We propose a novel time-resolved twisted x-ray diffraction technique that can directly monitor the electronic coherences created as the molecule passes through a conical intersection. We show that the contribution of electronic populations to this signal is canceled out when using twisted x-ray beams that carry a light orbital angular momentum, providing a direct measurement of transient electronic coherences in gas-phase molecules.

Ultrafast electron diffraction from transiently aligned asymmetric top molecules: Rotational dynamics and structure retrieval

Ultrafast electron diffraction (UED) from aligned molecules in the gas phase has successfully retrieved structures of both linear and symmetric top molecules. Alignment of asymmetric tops has been recorded with UED but no structural information was retrieved. We present here the extraction of two-dimensional structural information from simple transformations of experimental diffraction patterns of aligned molecules as a proof-of-principle for the recovery of the full structure. We align 4-fluorobenzotrifluoride with a linearly polarized laser and show that we can distinguish between atomic pairs with equal distances that are parallel and perpendicular to the aligned axis. We additionally show with numerical simulations that by cooling the molecules to a rotational temperature of 1 K, more distances and angles can be resolved through direct transformations.

Multichannel photodissociation dynamics in CS2 studied by ultrafast electron diffraction

The structural dynamics of photoexcited gas-phase carbon disulfide (CS₂) molecules are investigated using ultrafast electron diffraction. The dynamics were triggered by excitation of the optically bright ¹B₂(¹Σ_u⁺) state by an ultraviolet femtosecond laser pulse centred at 200 nm. In accordance with previous studies, rapid vibrational motion facilitates a combination of internal conversion and intersystem crossing to lower-lying electronic states. Photodissociation via these electronic manifolds results in the production of CS fragments in the electronic ground state and dissociated singlet and triplet sulphur atoms. The structural dynamics are extracted from the experiment using a trajectory-fitting filtering approach, revealing the main characteristics of the singlet and triplet dissociation pathways. Finally, the effect of the time-resolution on the experimental signal is considered and an outlook to future experiments provided.

Photoactivation of triosmium dodecacarbonyl at 400 nm probed with time-resolved X-ray liquidography

The photoactivation mechanism of Os₃(CO)₁₂ at 400 nm is examined with time-resolved X-ray liquidography. The data reveal two pathways: the vibrational relaxation following an internal conversion to the electronic ground state and the ligand dissociation to form Os₃(CO)₁₁ with a ligand vacancy at the axial position.

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

Time-Resolved Optical Pump-Resonant X-ray Probe Spectroscopy of 4-Thiouracil: A Simulation Study

We theoretically monitor the photoinduced ππ* → nπ* internal conversion process in 4-thiouracil (4TU), triggered by an optical pump. The element-sensitive spectroscopic signatures are recorded by a resonant X-ray probe tuned to the sulfur, oxygen, or nitrogen K-edge. We employ high-level electronic structure methods optimized for core-excited electronic structure calculation combined with quantum nuclear wavepacket dynamics computed on two relevant nuclear modes, fully accounting for their quantum nature of nuclear motions. We critically discuss the capabilities and limitations of the resonant technique. For sulfur and nitrogen, we document a pre-edge spectral window free from ground-state background and rich with ππ* and nπ* absorption features. The lowest sulfur K-edge shows strong absorption for both ππ* and nπ*. In the lowest nitrogen K-edge window, we resolve a state-specific fingerprint of the ππ* and an approximate timing of the conical intersection via its depletion. A spectral signature of the nπ* transition, not accessible by UV-vis spectroscopy, is identified. The oxygen K-edge is not sensitive to molecular deformations and gives steady transient absorption features without spectral dynamics. The ππ*/nπ* coherence information is masked by more intense contributions from populations. Altogether, element-specific time-resolved resonant X-ray spectroscopy provides a detailed picture of the electronic excited-state dynamics and therefore a sensitive window into the photophysics of thiobases.

Acousto-optically driven lensless single-shot ultrafast optical imaging

Driven by many applications in a wide span of scientific fields, a myriad of advanced ultrafast imaging techniques have emerged in the last decade, featuring record-high imaging speeds above a trillion-frame-per-second with long sequence depths. Although bringing remarkable insights into various ultrafast phenomena, their application out of a laboratory environment is however limited in most cases, either by the cost, complexity of the operation or by heavy data processing. We then report a versatile single-shot imaging technique combining sequentially timed all-optical mapping photography (STAMP) with acousto-optics programmable dispersive filtering (AOPDF) and digital in-line holography (DIH). On the one hand, a high degree of simplicity is reached through the AOPDF, which enables full control over the acquisition parameters via an electrically driven phase and amplitude spectro-temporal tailoring of the imaging pulses. Here, contrary to most single-shot techniques, the frame rate, exposure time, and frame intensities can be independently adjusted in a wide range of pulse durations and chirp values without resorting to complex shaping stages, making the system remarkably agile and user-friendly. On the other hand, the use of DIH, which does not require any reference beam, allows to achieve an even higher technical simplicity by allowing its lensless operation but also for reconstructing the object on a wide depth of field, contrary to classical techniques that only provide images in a single plane. The imaging speed of the system as well as its flexibility are demonstrated by visualizing ultrashort events on both the picosecond and nanosecond timescales. The virtues and limitations as well as the potential improvements of this on-demand ultrafast imaging method are critically discussed.

Toward fully automated UED operation using two-stage machine learning model

To demonstrate the feasibility of automating UED operation and diagnosing the machine performance in real time, a two-stage machine learning (ML) model based on self-consistent start-to-end simulations has been implemented. This model will not only provide the machine parameters with adequate precision, toward the full automation of the UED instrument, but also make real-time electron beam information available as single-shot nondestructive diagnostics. Furthermore, based on a deep understanding of the root connection between the electron beam properties and the features of Bragg-diffraction patterns, we have applied the hidden symmetry as model constraints, successfully improving the accuracy of energy spread prediction by a factor of five and making the beam divergence prediction two times faster. The capability enabled by the global optimization via ML provides us with better opportunities for discoveries using near-parallel, bright, and ultrafast electron beams for single-shot imaging. It also enables directly visualizing the dynamics of defects and nanostructured materials, which is impossible using present electron-beam technologies.

Ultrafast Imaging of Molecular Dynamics Using Ultrafast Low-Frequency Lasers, X-ray Free Electron Lasers, and Electron Pulses

The requirement of high space-time resolution and brightness is a great challenge for imaging atomic motion and making molecular movies. Important breakthroughs in ultrabright tabletop laser, X-ray, and electron sources have enabled the direct imaging of evolving molecular structures in chemical processes, and recent experimental advances in preparing ultrafast laser and electron pulses resulted in molecular imaging with femtosecond time resolution. This Perspective presents an overview of the versatile imaging methods of molecular dynamics. High-order harmonic generation imaging and photoelectron diffraction imaging are based on laser-induced ionization and rescattering processes. Coulomb explosion imaging retrieves molecular structural information by detecting the momentum vectors of fragmented ions. Diffraction imaging encodes molecular structural and electronic information in reciprocal space. We also present various applications of these ultrafast imaging methods in resolving laser-induced nuclear and electronic dynamics.

Determining the charge distribution and the direction of bond cleavage with femtosecond anisotropic x-ray liquidography

Energy, structure, and charge are fundamental quantities characterizing a molecule. Whereas the energy flow and structure change in chemical reactions are experimentally characterized, determining the atomic charges of a molecule in solution has been elusive, even for a triatomic molecule such as triiodide ion, I3-. Moreover, it remains to be answered how the charge distribution is coupled to the molecular geometry; which I-I bond, if two I-I bonds are unequal, dissociates depending on the electronic state. Here, femtosecond anisotropic x-ray solution scattering allows us to provide the following answers in addition to the overall rich structural dynamics. The analysis unravels that the negative charge of I3- is highly localized on the terminal iodine atom forming the longer bond with the central iodine atom, and the shorter I-I bond dissociates in the excited state, whereas the longer one in the ground state. We anticipate that this work may open a new avenue for studying the atomic charge distribution of molecules in solution and taking advantage of orientational information in anisotropic scattering data for solution-phase structural dynamics.

Investigating charge-up and fragmentation dynamics of oxygen molecules after interaction with strong X-ray free-electron laser pulses

The X-ray-induced charge-up and fragmentation process of a small molecule is examined in great detail by measuring the molecular-frame photoelectron interference pattern in conjunction with other observables in coincidence.

Few-fs resolution of a photoactive protein traversing a conical intersection

The structural dynamics of a molecule are determined by the underlying potential energy landscape. Conical intersections are funnels connecting otherwise separate potential energy surfaces. Posited almost a century ago¹, conical intersections remain the subject of intense scientific interest^2-5. In biology, they have a pivotal role in vision, photosynthesis and DNA stability⁶. Accurate theoretical methods for examining conical intersections are at present limited to small molecules. Experimental investigations are challenged by the required time resolution and sensitivity. Current structure-dynamical understanding of conical intersections is thus limited to simple molecules with around ten atoms, on timescales of about 100 fs or longer⁷. Spectroscopy can achieve better time resolutions⁸, but provides indirect structural information. Here we present few-femtosecond, atomic-resolution videos of photoactive yellow protein, a 2,000-atom protein, passing through a conical intersection. These videos, extracted from experimental data by machine learning, reveal the dynamical trajectories of de-excitation via a conical intersection, yield the key parameters of the conical intersection controlling the de-excitation process and elucidate the topography of the electronic potential energy surfaces involved.

Ultrafast Imaging of Molecules with Electron Diffraction

Photoexcited molecules convert light into chemical and mechanical energy through changes in electronic and nuclear structure that take place on femtosecond timescales. Gas phase ultrafast electron diffraction (GUED) is an ideal tool to probe the nuclear geometry evolution of the molecules and complements spectroscopic methods that are mostly sensitive to the electronic state. GUED is a passive probing tool that does not alter the molecular properties during the probing process and is sensitive to the spatial distribution of charge in the molecule, including both electrons and nuclei. Improvements in temporal resolution have enabled GUED to capture coherent nuclear motions in molecules in the excited and ground electronic states with femtosecond and subangstrom resolution. Here we present the basic theory of GUED and explain what information is encoded in the diffraction signal, review how GUED has been used to observe coherent structural dynamics in recent experiments, and discuss the advantages and limitations of the method. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

High density molecular jets of complex neutral organic molecules with Tesla valves

Supersonic jets of gas-phase atoms and small molecules have enabled a variety of ultrafast and ultracold chemical studies. However, extension to larger, more complex neutral molecules proves challenging for two reasons: (i) Complex molecules, such as cis-stilbene, exist in a liquid or solid phase at room temperature and ambient pressure and (ii) a unidirectional flow of high-density gaseous beams of such molecules to the interaction region is required. No delivery system currently exists that can deliver dense enough molecular jets of neutral complex molecules without ionizing or exciting the target for use in gas-phase structural dynamics studies. Here, we present a novel delivery system utilizing Tesla valves, which generates more than an order-of-magnitude denser gaseous beam of molecules compared to a bubbler without Tesla valves at the interaction region by ensuring a fast unidirectional flow of the gaseous sample. We present combined experimental and flow simulations of the Tesla valve setup. Our results open new possibilities of studying large complex neutral molecules in the gas-phase with low vapor pressures in future ultrafast and ultracold studies.

Quantum state tomography of molecules by ultrafast diffraction

Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments capture only the probability density of the nuclear wavepackets to determine the time-dependent molecular structures, while the full quantum state has not been accessed. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the molecular quantum states. The ability to reconstruct the density matrix, which encodes the amplitude and phase of the wavepacket, for molecules of arbitrary degrees of freedom, will enable the reconstruction of a quantum molecular movie from experimental x-ray or electron diffraction data.

Ultrafast diffraction is fundamental in capturing the structural dynamics of molecules. Here, the authors establish a variant of quantum state tomography for arbitrary degrees of freedom to characterize the molecular quantum states, which will enable the reconstruction of a quantum molecular movie from diffraction data.

Diffractive Imaging of Conical Intersections Amplified by Resonant Infrared Fields

The fate of virtually all photochemical reactions is determined by conical intersections. These are energetically degenerate regions of molecular potential energy surfaces that strongly couple electronic states, thereby enabling fast relaxation channels. Their direct spectroscopic detection relies on weak features that are often buried beneath stronger, less interesting contributions. For azobenzene photoisomerization, a textbook photochemical reaction, we demonstrate how a resonant infrared field can be employed during the conical intersection passage to significantly enhance its coherence signatures in time-resolved X-ray diffraction while leaving the product yield intact. This transition-state amplification holds promise to bring signals of conical intersections above the detection threshold.

Time-Resolved Photoelectron Spectroscopy of Conical Intersections with Attosecond Pulse Trains

Conical Intersections (CIs), which are believed to be ubiquitous in molecular and biological systems, open up ultrafast nonradiative decay channels. A superposition of electronic states is created when a molecule passes through a CI and the nuclear wave packet branches. The resulting electronic coherence can be considered a unique signature of the CI. The involved electronic states can be resolved in the energy domain with photoelectron spectroscopy using a femtosecond pulse as a probe. However, the observation of the created electronic coherence in the time domain requires probe pulses with several electron volts of bandwidth. Attosecond pulses can probe the electronic coherence but are unable to resolve the involved electronic states. In this Letter, we propose to address this restriction by using time-resolved photoelectron spectroscopy with an attosecond pulse train as a probe. We theoretically demonstrate that the resulting photoelectron spectrum may yield energy resolution as well as the information on the created coherences in the time domain.

Filming ultrafast roaming-mediated isomerization of bismuth triiodide in solution

Roaming reaction, defined as a reaction yielding products via reorientational motion in the long-range region (3 - 8 Å) of the potential, is a relatively recently proposed reaction pathway and is now regarded as a universal mechanism that can explain the unimolecular dissociation and isomerization of various molecules. The structural movements of the partially dissociated fragments originating from the frustrated bond fission at the onset of roaming, however, have been explored mostly via theoretical simulations and rarely observed experimentally. Here, we report an investigation of the structural dynamics during a roaming-mediated isomerization reaction of bismuth triiodide (BiI₃) in acetonitrile solution using femtosecond time-resolved x-ray liquidography. Structural analysis of the data visualizes the atomic movements during the roaming-mediated isomerization process including the opening of the Bi-I_b-I_c angle and the closing of I_a-Bi-I_b-I_c dihedral angle, each by ~40°, as well as the shortening of the I_b···I_c distance, following the frustrated bond fission.

Determination of excited state molecular structures from time-resolved gas-phase X-ray scattering

We present a comprehensive investigation of a recently introduced method to determine transient structures of molecules in excited electronic states with sub-ångstrom resolution from time-resolved gas-phase scattering signals. The method, which is examined using time-resolved X-ray scattering data measured on the molecule N-methylmorpholine (NMM) at the Linac Coherent Light Source (LCLS), compares the experimentally measured scattering patterns against the simulated patterns corresponding to a large pool of molecular structures to determine the full set of structural parameters. In addition, we examine the influence of vibrational state distributions and find the effect negligible within the current experimental detection limits, despite that the molecules have a comparatively high internal vibrational energy. The excited state structures determined using three structure pools generated using three different computational methods are in good agreement, demonstrating that the procedure is largely independent of the computational chemistry method employed as long as the pool is sufficiently expansive in the vicinity of the sought structure and dense enough to yield good matches to the experimental patterns.