Looking beyond one-dimensional distances in ultrafast liquid electron diffraction
image: Figure 1. ARPDF preserves angle information from anisotropic diffraction patterns, enabling more direct structural retrieval than conventional 1D PDF analysis.
Credit: Ultrafast Science
Researchers from Tsinghua University have developed a new angle-resolved analysis method for ultrafast liquid electron diffraction, offering a route to retrieve more complete three-dimensional structural dynamics from time-resolved diffraction data. The study, titled “Pair Distribution Function Beyond Isotropy: Angle-Resolved Analysis for Ultrafast Liquid Diffraction,” has been accepted by Ultrafast Science.
Ultrafast electron diffraction and time-resolved X-ray diffraction can capture molecular structural changes after photoexcitation with femtosecond temporal resolution. For liquids and gases, these data are usually analyzed using the isotropic pair distribution function, or PDF, which describes one-dimensional atomic distances but averages out angular information. This simplification can become limiting when molecules are excited by a linearly polarized laser, because photoselection creates an anisotropic excited-state ensemble.
To address this problem, the team focused on the angle-resolved pair distribution function, or ARPDF. Unlike conventional PDF analysis, ARPDF preserves both radial and angular structural correlations, allowing anisotropic diffraction signals to be interpreted more directly in real space. Although ARPDF has been used in gas-phase studies, its application to liquids has been difficult because strong intermolecular scattering can overlap with and obscure intramolecular structural signals.
In this work, the authors developed Angle-Resolved GPU-accelerated Optimization for LIquid Structure, or ARGOLIS, a generalized optimization method designed for ARPDF-based liquid structure retrieval. The method is also compatible with traditional PDF fitting, making it possible to directly compare the two approaches under the same framework.
Using simulated ultrafast electron diffraction data for liquid carbon tetrachloride, CCl4, the researchers showed that ARPDF-based fitting can reconstruct both intramolecular and intermolecular structural changes with high accuracy. In contrast, conventional PDF-based fitting may yield structurally ambiguous results even when the overall fit quality appears satisfactory. The study also showed that the fitting results remain stable when thermal motions are considered.
“Our goal is to move beyond observing only how atomic distances change,” said Prof. Jie Yang. “By using the angular information already contained in anisotropic diffraction patterns, we hope to reconstruct molecular motion in liquids in a more direct and physically meaningful way.”
This work establishes a methodological foundation for future liquid-phase ultrafast diffraction experiments that aim to use anisotropic signals for three-dimensional structural retrieval. As higher-quality time-resolved diffraction data become available, ARPDF and ARGOLIS may help researchers investigate photoinduced reactions, solvation dynamics, and nonequilibrium structural evolution in complex liquid environments.
The paper was authored by Jiayue Wang, Weizhi Shao, Keke Chen, Shijie Zheng, Chenglong Bao, and Jie Yang. The authors are affiliated with the Center of Basic Molecular Science, Department of Chemistry, Tsinghua University; the Yau Mathematical Sciences Center, Tsinghua University; and the Beijing Institute of Mathematical Sciences and Applications.