Machine learning for laser-induced electron diffraction imaging of molecular structures

Xinyao Liu,Tobias Steinle,Aurelien Sanchez,Blanca Belsa,Jens Biegert,Kasra Amini

doi:10.1038/s42004-021-00594-z

Abstract

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 limited set of molecular configurations. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C10H16O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. Retrieval of such a large molecular structure is not possible with other variants of LIED or ultrafast electron diffraction. Combining electron diffraction with machine learning presents new opportunities to image complex and larger molecules in static and time-resolved studies.

Highlights

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gasphase molecules with combined picometre spatial and attosecond temporal resolution
These fringe patterns are unique to the individual molecular configuration, making it significantly easier for the machine algorithm and its neural network to find the relationship between the molecular structures and their corresponding 2D-DCS maps
We showed that this permits machine learning (ML)-laser-induced electron diffraction (LIED) to reveal the 3D location of each atom in the molecule, providing significantly more detailed structural information than any other method that relies on the identification of non-overlapping peaks in the scattering radial distribution function

Summary

Introduction

Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gasphase molecules with combined picometre spatial and attosecond temporal resolution. We demonstrate structural retrieval of a complex and large molecule, Fenchone (C10H16O), from laser-induced electron diffraction (LIED) data without fitting algorithms or ab initio calculations. We note that similar problems arise in essentially all implementations of structural imaging and many retrieval algorithms severely limit the size of the molecular system under investigation To overcome these limitations, we employ a machine learning (ML) algorithm for LIED (ML-LIED) to accurately extract the three-dimensional (3D) molecular structure of larger and more complex molecules. Our ML model, together with the CNN algorithm and regression method, provides a new way forward to identify the structure of large complex molecules and transient structures with similar geometric configurations in time-resolved pump-probe measurements. We discuss the advantages, limitations, and many applications of the ML framework in retrieving large complex gas-phase molecular structures in the context of structural retrieval and time-resolved imaging of chemical reactions

Methods

Results

Conclusion