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

Abstract

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.

FIG. 1.

(a) Laser-induced electron diffraction is explained in three steps: (i) Tunnel ionization of the molecule at the time of ionization (birth) t_b, (ii) propagation of the electron wave packet (EWP) within the laser field, and (iii) scattering of the EWP at the electron's return time t_r. (b) The measured electron's momentum, k (green arrow), is defined in the laboratory frame (black solid coordinate system). In contrast, the returning momentum k_r (blue arrow) and the scattering angle ${\theta }_r$ of the electrons are given in the laser polarization frame (dashed coordinates).

FIG. 2.

Overview of different retrieval algorithms. QRS-, FT-, and ML-LIED are based on the extraction of field-free DCS in the laser polarization frame (a). By analyzing oscillation embedded in the DCS, the so-called molecular contrast factor (MCF), as a function of momentum transfer for either a fixed rescattering energy (QRS) (b) and (c) or a fixed rescattering angle (FT) (d)–(f), molecular bond lengths are retrieved. The 2D-DCS (g) is the input on the ML algorithms (h) and (i). Data are exemplary shown on C₂H₂⁺. ZCP-LIED can extract the bond directly in the scattering frame (j) through analysis of the zero-crossing points (k), and the data retrieval is shown in the example of OCS⁺. More details are found in the text. Figures are adapted from Refs. , , , and .

FIG. 3.

Scheme of a reaction microscope. A supersonic expansion into vacuum leads to molecules whose nuclear degrees of freedoms are essentially frozen. Skimmers reduce the target density such that maximally one molecule is interrogated by one laser pulse. TI leads to liberation of one electron which may scatter of the molecular ion. A magnetic field separated positively from negatively charged particles. A magnetic field is superimposed to increase detection to full 3D by projecting positive and negatively charged to delay line detectors with multi-hit detection capacity. Shown here is the simplest case of single ionization and no fragmentation of the molecular ion. Higher-order effects such as double ionization or multiple electrons are readily detected. Effects such as delayed ionization and fragmentation are also detectable. Fragments can be used to post-orient the molecule without alignment fields. For a comprehensive understanding of REMI's functionality and capabilities, we refer to Refs. , , and .

FIG. 4.

LIED visualizes the dynamics of field-dressed molecules. The strong field acts as a probing mechanism, allowing LIED to capture an instant depiction of the altered molecular structure 7–9 fs after ionization. This concept is exemplified using CS₂ as an illustration (a). In this manner, LIED provides intricate insights into various physical phenomena, including the Renner–Teller effect observed in CS₂ (b), the umbrella motion of NH₃⁺ (c), and the field-induced dipole enhancement through stretching and bending of H₂O (d). For more details, we refer to the text. Figures (a) and (b) are adapted from Amini et al., Proc. Natl. Acad. Sci. U. S. A. 116(17), 8173–8177 (2019). Copyright 2019 National Academy of Sciences. Figure (c) is reproduced with permission from Struct. Dyn. 8(1), 014301 (2021). Copyright 2021 AIP Publishing LLC and Figure (d) is adapted from Ref. .

FIG. 5.

Structure retrieval of the complex molecular structure of fenchone applying ML-LIED. (a) The Pearson correlation coefficient of 0.94 between the experimental and theoretical 2D-DCS calculated based on the ML algorithms' predicted structure shows a strong correlation. The predicted 3D position of seven fenchone (b) atoms compared to the equilibrium structure. Providing a visual representation, the predicted positions with their error bars (blue circles) are overlayed with the 3D molecular structure (c). Adapted with permission from Liu et al., Commun. Chem. 4(1), 154 (2021). Copyright 2021 Springer Nature.