Generative Modeling Enables Molecular Structure Retrieval from Coulomb Explosion Imaging

2025-10-31

AI Summary

In Coulomb explosion imaging, high-precision reconstruction of multiatomic molecular geometries from ion momentum distributions constitutes a highly nonlinear inverse problem; existing methods fail to achieve sub-bond-length accuracy. This work introduces, for the first time, a neural network framework that integrates diffusion models with a Transformer architecture to directly learn the nonlinear mapping from momentum distributions to 3D molecular configurations. Trained on high-repetition-rate experimental data from X-ray free-electron lasers (XFELs), the model achieves geometric reconstructions with a mean absolute error <0.5 Å (≈1 Bohr radius) across diverse multiatomic molecules—surpassing bond-length resolution. By circumventing the limitations of conventional iterative or analytical inversion approaches, our method enables real-time, high-fidelity tracking of molecular structural changes during ultrafast chemical reactions. It establishes a new paradigm for attosecond-scale structural dynamics studies.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

Abstract

Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly non-linear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.

Problem

• Retrieving molecular structures from Coulomb explosion imaging data
• Solving non-linear inverse problem of ion-momentum distributions
• Reconstructing molecular geometries with sub-chemical bond accuracy

Innovation

• Uses diffusion-based Transformer neural network
• Retrieves molecular structures from ion-momentum distributions
• Achieves sub-chemical bond length reconstruction accuracy