Extracting conformational structure information of benzene molecules via laser-induced electron diffraction

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.

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.

Directly imaging excited state-resolved transient structures of water induced by valence and inner-shell ionisation

Real-time imaging of transient structure of the electronic excited state is fundamentally critical to understand and control ultrafast molecular dynamics. The ejection of electrons from the inner-shell and valence level can lead to the population of different excited states, which trigger manifold ultrafast relaxation processes, however, the accurate imaging of such electronic state-dependent structural evolutions is still lacking. Here, by developing the laser-induced electron recollision-assisted Coulomb explosion imaging approach and molecular dynamics simulations, snapshots of the vibrational wave-packets of the excited (A) and ground states (X) of D2O+ are captured simultaneously with sub-10 picometre and few-femtosecond precision. We visualise that θDOD and ROD are significantly increased by around 50∘ and 10 pm, respectively, within approximately 8 fs after initial ionisation for the A state, and the ROD further extends 9 pm within 2 fs along the ground state of the dication in the present condition. Moreover, the ROD can stretch more than 50 pm within 5 fs along autoionisation state of dication. The accuracies of the results are limited by the simulations. These results provide comprehensive structural information for studying the fascinating molecular dynamics of water, and pave the way towards to make a movie of excited state-resolved ultrafast molecular dynamics and light-induced chemical reaction.

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.

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

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 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 relatively high sensitivity to hydrogen scattering. Here, we image the umbrella motion of an isolated ammonia molecule (NH₃) following its strong-field ionization. Upon ionization of a neutral ammonia molecule, the ammonia cation (NH₃ ⁺) undergoes an ultrafast geometrical transformation from a pyramidal ( Φ HNH = 107 ° ) to planar ( Φ HNH = 120 ° ) structure in approximately 8 femtoseconds. Using LIED, we retrieve a near-planar ( Φ HNH = 117   ±   5 ° ) field-dressed NH₃ ⁺ molecular structure 7.8 - 9.8 femtoseconds after ionization. Our measured field-dressed NH₃ ⁺ structure is in excellent agreement with our calculated equilibrium field-dressed structure using quantum chemical ab initio calculations.

Evolution of a Molecular Shape Resonance along a Stretching Chemical Bond

We report experiments on laser-assisted electron recollisions that result from strong-field ionization of photoexcited I_{2} molecules in the regime of low-energy electron scattering (<25  eV impact energy). By comparing differential scattering cross sections extracted from the angle-resolved photoelectron spectra to differential scattering cross sections from quantum-scattering calculations, we demonstrate that the electron-scattering dynamics is dominated by a shape resonance. When the molecular bond stretches during the evolution of a vibrational wave packet this shape resonance shifts to lower energies, both in experiment and theory. We explain this behavior by the nature of the resonance wave function, which closely resembles an antibonding molecular orbital of I_{2}.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses.

Symphony on strong field approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the 'simple man's models' which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include high-harmonic generation (HHG), above-threshold ionization (ATI), and non-sequential multielectron ionization (NSMI). 'Simple man's models' provide both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation and the motivation for the powerful analytic approximations generally known as the strong field approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach the SFA is a method to solve the TDSE, in which the non-perturbative interactions are described by including continuum-continuum interactions in a systematic perturbation-like theory. In this review we focus on recent applications of the SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom molecules. The main novel part of the presented theory concerns generalizations of the SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between electron impact ionization and resonant excitation with subsequent ionization; (ii) time-dependent treatment in the single active electron approximation of 'large' molecules and targets which are themselves undergoing dynamics during the HHG or ATI processes. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields. We dedicate this work to the memory of Bertrand Carré, who passed away in March 2018 at the age of 60.

Probing gaseous molecular structure by molecular-frame photoelectron angular distributions

Carbon 1s photoelectron angular distributions of an iodomethane molecule were measured relative to the recoil-frame determined by the momentum correlation between I⁺ and CH₃ ⁺ at photoelectron energies of 3, 6.1, and 12 eV. The energy dependent behavior of the recoil-frame photoelectron angular distributions is reproduced reasonably well by the time-dependent density functional theory with B-spline methods. We discuss potential applications of the fully differential photoelectron angular distribution measurements in the molecular frame to three-dimensional molecular structural determinations identifying the directions and lengths of the bonds.

Imaging an isolated water molecule using a single electron wave packet

Observing changes in molecular structure requires atomic-scale Ångstrom and femtosecond spatio-temporal resolution. We use the Fourier transform (FT) variant of laser-induced electron diffraction (LIED), FT-LIED, to directly retrieve the molecular structure of H₂O⁺ with picometer and femtosecond resolution without a priori knowledge of the molecular structure nor the use of retrieval algorithms or ab initio calculations. We identify a symmetrically stretched H₂O⁺ field-dressed structure that is most likely in the ground electronic state. We subsequently study the nuclear response of an isolated water molecule to an external laser field at four different field strengths. We show that upon increasing the laser field strength from 2.5 to 3.8 V/Å, the O-H bond is further stretched and the molecule slightly bends. The observed ultrafast structural changes lead to an increase in the dipole moment of water and, in turn, a stronger dipole interaction between the nuclear framework of the molecule and the intense laser field. Our results provide important insights into the coupling of the nuclear framework to a laser field as the molecular geometry of H₂O⁺ is altered in the presence of an external field.

Atomic-resolution imaging of carbonyl sulfide by laser-induced electron diffraction

Measurements on the strong-field ionization of carbonyl sulfide molecules by short, intense, 2 µm wavelength laser pulses are presented from experiments where angle-resolved photoelectron distributions were recorded with a high-energy velocity map imaging spectrometer, designed to reach a maximum kinetic energy of 500 eV. The laser-field-free elastic-scattering cross section of carbonyl sulfide was extracted from the measurements and is found in good agreement with previous experiments, performed using conventional electron diffraction. By comparing our measurements to the results of calculations, based on the quantitative rescattering theory, the bond lengths and molecular geometry were extracted from the experimental differential cross sections to a precision better than ±5 pm and in agreement with the known values.

Probing Attosecond Electron Coherence in Molecular Charge Migration by Ultrafast X-Ray Photoelectron Imaging

Electron coherence is a fundamental quantum phenomenon in today’s ultrafast physics and chemistry research. Based on attosecond pump–probe schemes, ultrafast X-ray photoelectron imaging of molecules was used to monitor the coherent electron dynamics which is created by an XUV pulse. We performed simulations on the molecular ion H 2 + by numerically solving time-dependent Schrödinger equations. It was found that the X-ray photoelectron angular and momentum distributions depend on the time delay between the XUV pump and soft X-ray probe pulses. Varying the polarization and helicity of the soft X-ray probe pulse gave rise to a modulation of the time-resolved photoelectron distributions. The present results provide a new approach for exploring ultrafast coherent electron dynamics and charge migration in reactions of molecules on the attosecond time scale.

Probing molecular bond-length using molecular-frame photoelectron angular distributions

The molecular-frame photoelectron angular distributions (MFPADs) in O 1s photoemission from CO₂ molecule were measured. Patterns due to photoelectron diffractions were observed in the MFPADs. The polarization-averaged MFPADs were compared with theoretical calculation and were found to be useful in determining the molecular bond-length, which is a component to determine molecular structures.

Diffractive Imaging of C_{60} Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100 fs (1  fs=10^{-15}  s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6  μm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

Molecular orbital imprint in laser-driven electron recollision

Electrons released by strong-field ionization from atoms and molecules or in solids can be accelerated in the oscillating laser field and driven back to their ion core. The ensuing interaction, phase-locked to the optical cycle, initiates the central processes underlying attosecond science. A common assumption assigns a single, well-defined return direction to the recolliding electron. We study laser-induced electron rescattering associated with two different ionization continua in the same, spatially aligned, polyatomic molecule. We show by experiment and theory that the electron return probability is molecular frame-dependent and carries structural information on the ionized orbital. The returning wave packet structure has to be accounted for in analyzing strong-field spectroscopy experiments that critically depend on the interaction of the laser-driven continuum electron, such as laser-induced electron diffraction.

Dynamics of valence-shell electrons and nuclei probed by strong-field holography and rescattering

Strong-field photoelectron holography and laser-induced electron diffraction (LIED) are two powerful emerging methods for probing the ultrafast dynamics of molecules. However, both of them have remained restricted to static systems and to nuclear dynamics induced by strong-field ionization. Here we extend these promising methods to image purely electronic valence-shell dynamics in molecules using photoelectron holography. In the same experiment, we use LIED and photoelectron holography simultaneously, to observe coupled electronic-rotational dynamics taking place on similar timescales. These results offer perspectives for imaging ultrafast dynamics of molecules on femtosecond to attosecond timescales.

Capturing ultrafast molecular dynamics is difficult as the process involves coupled and very fast motions of electrons and nuclei. Here the authors study non-adiabatic dynamics in the NO molecule using strong-field photoelectron holography to shed light on the valence-shell electron dynamics.