Generative Modeling Enables Molecular Structure Retrieval from Coulomb Explosion Imaging

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.

Figures (4)

• Figure 1: Generative-modeling-enabled molecular structure retrieval from Coulomb explosion imaging.a, Illustration of the Coulomb explosion imaging technique and the molecular structure retrieval from its momentum measurements using the MOLEXA neural network. The main architectural details of MOLEXA are displayed in panels b and c. The ball-and-stick models in this and the subsequent figures represent the scaled spatial arrangement of the atomic constituents in the molecules. b, Dynamics extraction module. c, Structure denoising module.
• Figure 2: Overview of MOLEXA's prediction accuracy and its relation to the predicted uncertainties. The columns from left to right represent molecules with an increasing number of atoms. Top row: Exemplary structure predictions with low predicted uncertainties. The predicted and ground-truth structures are plotted as opaque and semi-transparent ball-and-stick models, respectively. The corresponding uncertainty, root mean squared error (RMSE), and mean absolute error (MAE) are listed below each molecular structure. The color coding of the elements is as follows - H: white, C: gray, N: blue, O: red, F: cyan, Si: brown, P: orange, S: yellow, and Cl: green. Second row: Corresponding structure predictions with high predicted uncertainties. The two bottom rows depict the dependence of the accuracy and the MAE on the predicted uncertainty (see text). The corresponding MOLEXA input data including the ion charge states and momentum distributions are shown in Supplementary Fig. \ref{['fig:S_momen_performance']}.
• Figure 3: Reconstruction of molecular geometries from experimental data.a, Molecular structure reconstruction of Water. The measured 2D momentum map is shown on the left. To its right is the illustration of the averaged momentum distribution of the three ion fragments, which is used as the input to MOLEXA. In the real space, the reconstructed and ground-truth structures are plotted as opaque and semi-transparent ball-and-stick models, respectively. b, Molecular structure reconstruction of tetrafluoromethane. c, Molecular structure reconstruction of ethanol. The corresponding orientations of the pre-explosion molecule are displayed at the top of the 2D momentum maps. The color coding of the elements is as follows - H: white, C: gray, O: red, and F: cyan.
• Figure 4: Reconstruction of structural changes.a, Reconstructed geometries of cyclobutene in its S$_0$ and S$_1$ states. b, Reconstructed "snapshots" of cyclobutene during a chemical reaction. The color coding of the elements is as follows - H: white, C: gray.