Knowledge of molecular structure is paramount in understanding, and ultimately influencing, chemical reactivity. For nearly a century, diffractive imaging has been used to identify the structures of many biologically-relevant gas-phase molecules with atomic (i.e. Angstrom, A; 1 A = 10$^{-10}$ m) spatial resolution. Unravelling the mechanisms of chemical reactions requires the capability to record multiple well-resolved snapshots of the molecular structure as it is evolving on the nuclear (i.e. femtosecond, fs; 1 fs = 10$^{-15}$ s) timescale. We present the latest, state-of-the-art ultrafast electron diffraction methods used to retrieve the molecular structure of gas-phase molecules with Angstrom and femtosecond spatio-temporal resolution. We first provide a historical and theoretical background to elastic electron scattering in its application to structural retrieval, followed by details of field-free and field-dressed ultrafast electron diffraction techniques. We discuss the application of these ultrafast methods to time-resolving chemical reactions in real-time, before providing a future outlook of the field and the challenges that exist today and in the future.
We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information of …
Free-electron laser hard X-ray light sources can provide high fluence, femtosecond pulses, enabling the time-resolved probing of structural dynamics and elementary relaxation processes in molecules. Traditional X-ray elastic scattering from crystals in the ground state consists of sharp Bragg diffraction peaks that arise from pairs of molecules and reveal the ground state charge density. Scattering of ultrashort X-ray pulses from gases, liquids, and even single molecules is more complex and involves both single- and two- molecule contributions, diffuse (non-Bragg) features, elastic and inelast…
The manipulation of the motion of neutral molecules with electric or magnetic fields has seen tremendous progress over the last decade. Recently, these techniques have been extended to the manipulation of large and complex molecules. In this article we introduce experimental approaches to the manipulation of large molecules, i.e., the deflection, focusing and deceleration using electric fields. We detail how these methods can be exploited to spatially separate quantum states and how to select individual conformers of complex molecules. We briefly describe mixed-field orientation experiments ma…
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 phot…
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 employ the classical "ball-and-stick" depictions, and the information of molecular quantum states, such as the density matrix, is missing. 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…
The ultrafast photoinduced ring-opening of 1,3-cyclohexadiene constitutes a textbook example of electrocyclic reactions in organic chemistry and a model for photobiological reactions in vitamin D synthesis. Here, we present direct and unambiguous observation of the ring-opening reaction path on the femtosecond timescale and sub-Ångström length scale by megaelectronvolt ultrafast electron diffraction. We follow the carbon-carbon bond dissociation and the structural opening of the 1,3-cyclohexadiene ring by direct measurement of time-dependent changes in the distribution of interatomic distances…
The competition between intra molecular charge redistribution and fragmentation has been studied in small molecules containing iodine by using intense ultrashort pulses in the extreme ultraviolet regime (XUV). We show that after an element specific inner-shell photoionization of diiodomethane (CH$_2$I$_2$) and iodomethane (CH$_3$I), the induced positive charge is redistributed with a significantly different efficiency. Therefore, we analyze ion time-of-flight data obtained from XUV-pump XUV-probe experiments at the Free Electron Laser in Hamburg (FLASH). Theoretical considerations on the basis…
Metal-corroles are macrocycle organic molecules with numerous practical applications. In particular, copper corroles exhibit an interesting saddled geometry, which has attracted significant attention from theoreticians and experimentalists over the years. The present work is dedicated to understand the effect of structural saddling in a copper corrole on potential probe signals via imaging ultrafast coherent electron dynamics. A linearly polarized pulse is used to trigger the electron dynamics and time-resolved x-ray diffraction is employed to image the triggered dynamics. It is found that the…
Visualizing molecular transformations in real-time requires a structural retrieval method with Ångström spatial and femtosecond temporal atomic resolution. Imaging of hydrogen-containing molecules additionally requires an imaging method that is sensitive to the atomic positions of hydrogen nuclei, with most methods possessing relatively low sensitivity to hydrogen scattering. Laser-induced electron diffraction (LIED) is a table top technique that can image ultrafast structural changes of gas-phase polyatomic molecules with sub-Ångström and femtosecond spatiotemporal resolution together with re…
We report a novel experimental technique to investigate ultrafast dynamics in photoexcited molecules by probing the third-order nonlinear optical susceptibility. A non-colinear 3-pulse scheme is developed to probe the ultrafast dynamics of excited electronic states using the optical Kerr effect by time-resolved polarization spectroscopy. Optical heterodyne and optical homodyne detection are demonstrated to measure the third-order nonlinear optical response for the S1 excited state of liquid nitrobenzene, which is populated by 2-photon absorption of a 780 nm 35 fs excitation pulse.
X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved X-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear X-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation c…
We describe an apparatus to study the fragmentation of ion-molecule clusters triggered by laser excitation and transfer of an electron from the iodide to the neutral molecule. The apparatus comprises a source to generate ion-molecule clusters, a time-of-flight (TOF) spectrometer and a mass filter to select the desired anions, and a linear-plus-quadratic reflectron mass spectrometer to discriminate the fragment anions after the femtosecond laser excites the clusters. The fragment neutrals and anions are then captured by two channeltron detectors. The apparatus performance is tested by measuring…
Conical intersections between electronic states often dictate the chemistry of photoexcited molecules. Recently developed sources of ultrashort extreme ultraviolet (XUV) pulses tuned to element-specific transitions in molecules allow for the unambiguous detection of electronic state-switching at a conical intersection. Here, the fragmentation of photoexcited iso-propyl iodide and tert-butyl iodide molecules (i-C$_{3}$H$_{7}$I and t-C$_{4}$H$_{9}$I) through a conical intersection between $^{3}$Q$_{0}$/$^{1}$Q$_{1}$ spin-orbit states is revealed by ultrafast XUV transient absorption measuring io…
Single molecule spectroscopy aims at unveiling often hidden but potentially very important contributions of single entities to a system's ensemble response. Albeit contributing tremendously to our ever growing understanding of molecular processes the fundamental question of temporal evolution, or change, has thus far been inaccessible, resulting in a static picture of a dynamic world. Here, we finally resolve this dilemma by performing the first ultrafast time-resolved transient spectroscopy on a single molecule. By tracing the femtosecond evolution of excited electronic state spectra of singl…
It is discussed how vibrationally excited molecules in their electronic ground state can transfer their vibrational energy to the electronic motion of neighbors and ionize them. Based on explicit examples of vibrationally excited molecules and anionic neighbors, it is demonstrated that the transfer can be extremely efficient at intermolecular distances much beyond distances at which the molecule and its neighbor can form a bond.
We applied angular X-ray Cross-Correlation analysis (XCCA) to scattering images from a femtosecond resolution LCLS X-ray free-electron laser (XFEL) pump-probe experiment with solvated PtPOP ([Pt$_2$(P$_2$O$_5$H$_2$)$_4$]$^{4-}$) metal complex molecules. The molecules were pumped with linear polarized laser pulses creating an excited state population with a preferred orientational (alignment) direction. Two time scales of $1.9\pm1.5$ ps and $46\pm10$ ps were revealed by model-independent XCCA, associated with an internal structural changes and rotational dephasing, respectively. Our studies ill…
A dc electron gun, generating picosecond pulses with up to $8\times10^{6}$ electrons per pulse, was developed. Its applicability for future time-resolved-diffraction experiments on state- and conformer-selected laser-aligned or oriented gaseous samples was characterized. The focusing electrodes were arranged in a velocity-map imaging spectrometer configuration. This allowed to directly measure the spatial and velocity distributions of the electron pulses emitted from the cathode. The coherence length and pulse duration of the electron beam were characterized by these measurements combined with…
This article presents the program module \texttt{RhoDyn} as part of the \texttt{OpenMolcas} project intended to study ultrafast electron dynamics within the density-matrix-based time-dependent restricted active space configuration interaction framework ($ρ$-TD-RASCI). The formalism allows for the treatment of spin-orbit coupling effects, accounts for nuclear vibrations in the form of a vibrational heat-bath, and naturally incorporates (auto)ionization effects. Apart from describing the theory behind and the program workflow, the paper also contains examples of its application to the simulation…
Impacts of Hot Electron Diffusion, Electron-Phonon Coupling, and Surface Atoms on Metal Surface Dynamics Revealed by Reflection Ultrafast Electron Diffraction
In the last two decades, the three-beams pump-push-probe (PPP) technique has become a well-established tool for investigating the multidimensional configurational space of a molecule, as it permits to disclose precious information about the multiple and often complex deactivation pathways of the excited molecule. From the spectroscopic point of view, such a tool has revealed details about the efficiency of charge pairs generation and conformational relaxation in p-conjugated molecules and macromolecules. In addition, PPP has been effectively utilised for modulating the gain signal in conjugate…
Calculations relating to two experiments that demonstrate coherent control of preformed rubidium-85 molecules in a magneto-optical trap using ultrafast laser pulses are presented. In the first experiment, it is shown that pre-associated molecules in an incoherent mixture of states can be made to oscillate coherently using a single ultrafast pulse. A mechanism that can transfer molecular population to more deeply bound vibrational levels is used in the second. Optimal parameters of the control pulse are presented for the application of the mechanism to molecules in a magneto-optical trap. The c…
We propose a strategy for enabling photodissociation of a normally photostable molecule through coupling to a nanoparticle plasmon. The large possible coupling on the single-molecule level combined with the highly lossy nature of plasmonic modes, with lifetimes on the order of femtoseconds, opens an ultrafast decay channel for the molecule. For plasmon mode frequencies below the vertical photoexcitation energy of the molecule, the difference between excitation and emission energy is converted into vibrational energy on the molecular ground state in a Raman-like process. Under the correct condi…
An $\mathit{ab\ initio}$ theory is devised for the quantum dynamics of molecules undergoing (multiple) ionization in ultrafast and intense light. Specifically, the intertwined problem of photoionization, radiative, and electronic transitions in the course of dissociation is addressed which arises, e.g., when molecules are exposed to XUV light or x rays from free electron lasers or attosecond light sources, but the approach is equally useful in optical strong-field physics. The coherent interaction of the molecule with the light in a specific charge state is also treated. I set out from an abst…
Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult with increasing structural complexity, given that a global extremum must be found in a multi-dimensional solution space. Worse, pre-calculating many thousands of molecular configurations for all orientations becomes simply intractable. As a remedy, here, we propose a machine learning algorithm with a convolutional neural network which can be trained with a lim…
An experimental pump-probe study of the photoassociative creation of translationally ultracold rubidium molecules is presented together with numerical simulations of the process. The formation of loosely bound excited-state dimers is observed as a first step towards a fully coherent pump-dump approach to the stabilization of Rb$_2$ into its lowest ground vibrational states. The population that contributes to the pump-probe process is characterized and found to be distinct from a background population of pre-associated molecules.
A CASSCF/MRCI Trajectory Surface Hopping Simulation of the Photochemical Dynamics and the Gas Phase Ultrafast Electron Diffraction Patterns of Cyclobutanone
The recently introduced synthetic chiral light [D. Ayuso et al, Nat. Photon. 13, 866-871 (2019)] has opened up new opportunities for ultrafast and highly efficient imaging and control of chiral matter. Here we show that the giant enantio-sensitivity enabled by such light could be exploited to probe chiral nuclear rearrangements during chemical reactions in an highly enantio-sensitive manner. Using a state-of-the-art implementation of time-dependent density functional theory, we explore how the nonlinear response of the prototypical chiral molecule H2O2 changes as a function of its dihedral ang…
Four-dimensional imaging of charge migration is crucial to the understanding of several ubiquitous processes in nature. The present work focuses on imaging of charge migration in an oriented epoxypropane: a chiral molecule. A linearly polarized pulse is used to induce the charge migration, which is imaged by time-resolved x-ray diffraction. It is found that the total time-resolved diffraction signals are significantly different for both enantiomers. Furthermore, a connection between time-resolved x-ray diffraction and the electronic continuity equation is discussed by analyzing the time-depend…
Photoelectron Angular Distributions (PADs) resulting from 800 nm and 1300 nm strong field ionization of impulsively aligned CF$_3$I molecules were analyzed using time-dependent density functional theory (TDDFT). The normalized difference between the PADs for aligned and anti-aligned molecules displays large modulations in the high-energy re-collision plateau that are assigned to the diffraction of back-scattered photoelectrons. The TDDFT calculations reveal that, in spite of their 2.6 eV energy difference, ionization from the HOMO-1 orbital contributes to the diffraction pattern on the same fo…
We present a general formalism of ultrafast diffractive voltammetry approach as a contact-free tool to investigate the ultrafast surface charge dynamics in nanostructured interfaces. As case studies, the photoinduced surface charging processes in oxidized silicon surface and the hot electron dynamics in nanoparticle-decorated interface are examined based on the diffractive voltammetry framework. We identify that the charge redistribution processes appear on the surface, sub-surface, and vacuum levels when driven by intense femtosecond laser pulses. To elucidate the voltammetry contribution fro…
Carrier envelope phase (CEP) stabilized pulses of intense 800 nm light of 5 fs duration are used to probe the dissociation dynamics of dications of isotopically-substituted water, HOD. HOD$^{2+}$ dissociates into either H$^+$ + OD$^+$ or D$^+$ + OH$^+$. The branching ratio for these two channels is CEP-dependent; the OD$^+$/OH$^+$ ratio (relative to that measured with CEP-unstabilized pulses) varies from 150% to over 300% at different CEP values, opening prospects of isotope-dependent control over molecular bond breakage. The kinetic energy released as HOD$^{2+}$ Coulomb explodes is also CEP-d…
Conventional approaches to probing ultrafast molecular dynamics rely on the use of synchronized laser pulses with a well-defined time delay. Typically, a pump pulse excites a wavepacket in the molecule. A subsequent probe pulse can then dissociates or ionizes the molecule, and measurement of the molecular fragments provides information about where the wavepacket was for each time delay. In this work, we propose to exploit the ultrafast nuclear-position-dependent emission obtained due to large light-matter coupling in plasmonic nanocavities to image wavepacket dynamics using only a single pump …
Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space $\left|σ(\mathbf{q})\right|^{2}$, missing its phase which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals $σ(\mathbf{q})$ itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diff…
Real-time time-dependent density functional theory, in conjunction with the Ehrenfest molecular dynamics scheme, is becoming a popular methodology to investigate ultrafast phenomena on the nanoscale. Thanks to recent developments, it is also possible to explicitly include in the simulations a time-dependent laser pulse, thereby accessing the transient excitation regime. However, the complexity entailed in these calculations calls for in-depth analysis of the accessible and yet approximate (either "dressed" or "bare") quantities, in order to evaluate their ability to provide us with a realistic…
