Laser-induced electron diffraction of the ultrafast umbrella motion in ammonia

Extraction of Molecular-Frame Electron-Ion Differential Scattering Cross Sections Based on Elliptical Laser-Induced Electron Diffraction

We extracted the molecular-frame elastic differential cross sections (MFDCSs) for electrons scattering from N_{2}^{+} based on elliptical laser-induced electron diffraction (ELIED), wherein the structural evolution is initialized by the same tunneling ionization and probed by incident angle-resolved laser-induced electron diffraction imaging. To establish ELIED, an intuitive interpretation of the ellipticity-dependent rescattering electron momentum distributions was first provided by analyzing the transverse momentum distribution. It was shown that the incident angle of the laser-induced returning electrons could be tuned within 20° by varying the ellipticity and handedness of the driving laser pulses. Accordingly, the incident angle-resolved DCSs of returning electrons for spherically symmetric targets (Xe^{+} and Ar^{+}) were successfully extracted as a proof-of-principle for ELIED. The MFDCSs for N_{2}^{+} were experimentally obtained at incident angles of 4° and 7°, which were well reproduced by the simulations. The ELIED approach is the only successful method so far for obtaining incident angle-resolved ionic MFDCS, which provides a new sensitive observable for the transient structure retrieval of N_{2}^{+}. Our results suggest that the ELIED has the potential to extract the structural tomographic information of polyatomic molecules with femtosecond and subangstrom spatiotemporal resolutions that can enable the visualization of the nuclear motions in complex chemical reactions as well as chiral recognition.

Ultrafast studies of elusive chemical reactions in the gas phase

The chemical composition of the interstellar medium and planetary atmospheres is constantly in flux as atoms and molecules collide and interact with high-energy particles such as electrons, protons, and photons. These transformative processes ultimately lead to the coalescence of molecules and eventually the birth of stars. Our understanding of these chemical ecosystems relies on models that synthesize data from gas-phase experiments, providing insights into reaction cross sections. This Review examines efforts to delve into the fundamental bond-forming and bond-breaking dynamics that occur during bimolecular and electron-initiated reactions. These experiments involve clever approaches to establish a time reference and the collision geometry necessary for tracking atomic motion with femtosecond time resolution. Findings from these efforts enhance present models and improve predictions for molecule-molecule and electron-molecule collisions.

Ultrafast Picometer-Resolved Molecular Structure Imaging by Laser-Induced High-Order Harmonics

Real-time visualization of molecular transformations is a captivating yet challenging frontier of ultrafast optical science and physical chemistry. While ultrafast x-ray and electron diffraction methods can achieve the needed subangstrom spatial resolution, their temporal resolution is still limited to hundreds of femtoseconds, much longer than the few femtoseconds required to probe real-time molecular dynamics. Here, we show that high-order harmonics generated by intense femtosecond lasers can be used to image molecules with few-ten-attosecond temporal resolution and few-picometer spatial resolution. This is achieved by exploiting the sensitive dependence of molecular recombination dipole moment to the geometry of the molecule at the time of harmonic emission. In a proof-of-principle experiment, we have applied this high-harmonic structure imaging (HHSI) method to monitor the structural rearrangement in NH_{3}, ND_{3}, and N_{2} from one to a few femtoseconds after the molecule is ionized by an intense laser. Our findings establish HHSI as an effective approach to resolve molecular dynamics with unprecedented spatiotemporal resolution, which can be extended to trace photochemical reactions in the future.

Laser-induced electron diffraction: Imaging of a single gas-phase molecular structure with one of its own electrons

Among the many methods to image molecular structure, laser-induced electron diffraction (LIED) can image a single gas-phase molecule by locating all of a molecule's atoms in space and time. The method is based on attosecond electron recollision driven by a laser field and can reach attosecond temporal resolution. Implementation with a mid-IR laser and cold-target recoil ion-momentum spectroscopy, single molecules are measured with picometer resolution due to the keV electron impact energy without ensemble averaging or the need for molecular orientation. Nowadays, the method has evolved to detect single complex and chiral molecular structures in 3D. The review will touch on the various methods to discuss the implementations of LIED toward single-molecule imaging and complement the discussions with noteworthy experimental findings in the field.

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.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Two-dimensional retrieval methods for ultrafast imaging of molecular structure using laser-induced electron diffraction

Molecular structural retrieval based on electron diffraction has been proposed to determine the atomic positions of molecules with sub-angstrom spatial and femtosecond temporal resolutions. Given its success on small molecular systems, in this work, we point out that the accuracy of structure retrieval is constrained by the availability of a wide range of experimental data in the momentum space in all molecular systems. To mitigate the limitations, for laser-induced electron diffraction, here we retrieve molecular structures using two-dimensional (energy and angle) electron momentum spectra in the laboratory frame for a number of small molecular systems, which have previously been studied with 1D methods. Compared to the conventional single-energy or single-angle analysis, our 2D methods effectively expand the momentum range of the measured data. Besides utilization of the 2D data, two complementary methods are developed for consistency check on the retrieved results. The 2D nature of our methods also offers a way of estimating the error from retrieval, which has never been explored before. Comparing with results from prior experiments, our findings show evidence that our 2D methods outperform the conventional 1D methods. Paving the way to the retrieval of large molecular systems, in which their tunneling ionization rates are challenging to obtain, we estimate the error of using the isotropic model in place of including the orientation-dependent ionization rate.

Umbrella inversion of ammonia redux

Umbrella inversion of ammonia is a prototypical example of large-amplitude vibrational motion, described with a symmetric double-well potential. The transition state of the latter corresponds to a planar (D_3h) molecular geometry, whereas the two equilibrium configurations are equivalent (C_3v) pyramidal structures, with the nitrogen atom being either 'above' or 'below' the plane of the hydrogen atoms. As commonly understood, inversion motion of ammonia corresponds to the coherent, anharmonic, vibrational motion of the molecule, which shuttles back and forth between the two potential wells; that is, oscillation of the nitrogen atom from one side of the H₃ plane to the other, via coherent tunneling. However, this intuitively appealing view of umbrella inversion results from a reduced description of the dynamics, which includes only the inversion vibrational coordinate and fully neglects all the other molecular degrees of freedom. As such, this textbook picture of inversion motion ignores the fact that the two equilibrium structures of ammonia are superimposable, and can only be distinguished by labelling the identical hydrogen nuclei. A correct description of umbrella inversion, which incorporates nuclear permutations, requires the inclusion of other molecular modes. Indeed, it is well known that the quantum symmetrization postulate engenders entanglement between ammonia's nuclear-spin, inversion, and rotation. Using the explicit expressions of the corresponding zeroth-order eigenstates, we clearly show that the inversion density of any multilevel wavepacket of ammonia, including the case of perfectly aligned molecules, is symmetrically distributed between the two potential wells, at all times. This follows from a rigorous demonstration based on the evaluation of the expectation values of the inversion coordinate or equivalent projection operators. However, provided that these wavepackets involve inversion-rotation levels with opposite parity, the inversion density may exhibit dynamical spatial localization. In the latter case, the space-fixed inversion density or, equivalently, the expectation values of the projections of the inversion coordinate on the space-fixed axes, may oscillate between opposite directions in the space-fixed frame. Nevertheless, in all cases, localization of ammonia in a single potential well is impossible, even partially or transiently. This is equivalent to saying that the nitrogen atom has the same probability (one-half) to be on either side of the H₃ plane, for any wavepacket of the molecule and at all times-a conclusion which is in perfect accord with the principle of the indistinguishability of identical particles (nuclei).