Neural Network Based Molecular Structure Retrieval from Coulomb Explosion Imaging Data

TL;DR

This work proposes a scheme to solve the underlying inverse problem by employing neural networks to infer the initial atomic positions from the final ion momenta on an event-by-event basis and retrieves the structure of several polyhalomethane isomers from simulated Coulomb explosion imaging data.

Abstract

Determining the structure and following the structural evolution of molecules undergoing chemical reactions is one of the key goals of ultrafast molecular physics and chemistry. Recently, Coulomb explosion imaging has emerged as a promising technique for imaging the evolving structure of individual molecules in the gas phase. However, its practical application for structure determination is hampered by the lack of suitable algorithms to directly retrieve the molecular structure from the measured fragment-ion momentum data. Here, we propose a scheme to solve the underlying inverse problem by employing neural networks to infer the initial atomic positions from the final ion momenta on an event-by-event basis. Using this scheme, we retrieve the structure of several polyhalomethane isomers from simulated Coulomb explosion imaging data with an average per-atom position error of approximately 0.1 atomic units, i.e., to within 5% of the typical bond lengths. This development paves the way for an automated structure retrieval from Coulomb explosion data one molecule at a time, making it ideally suitable for analyzing pump-probe experiments where several products are formed that need to be distinguished.

Figures (5)

• Figure 1: Schematic of the molecular structure reconstruction approach: A neural network is used to reconstruct the molecular structure of various CHBrClF isomers from the three-dimensional fragment-ion momenta resulting from the Coulomb explosion induced by a femtosecond laser pulse.
• Figure 2: Schematic representation of a fully connected Multilayer Perceptron (MLP) architecture. The network consists of an input layer that accepts the input data $\mathbf{y}$. The data are transformed through a sequence of layers via Eq. \ref{['eq:layer-transformation']} to produce the final output $\mathbf{\hat{x}}$. The weights, $W^{(k)}$ and biases, $\mathbf{b}^{(k)}$ control how each layer transforms its inputs. These parameters are learned during training.
• Figure 3: Ball-and-stick-models of the eight CHBrClF isomers used to test the real-space reconstruction model. The open circles mark the center of mass of the initial position-space distribution used as a starting point for the Coulomb explosion simulations ("ground truth"). The diamonds mark the center of mass of the retrieved position-space distribution. For the results shown here, isomer (d) was not part of the training dataset. The crosses in (d) mark the results for the case where the random-positions-in-sphere data was added to the training data.
• Figure 4: Initial (blue) and predicted (orange) position distributions for all atoms of (a) the original CHBrClF molecule and (b) for the isomer that was left out of the training data. In panel (b), the red lines show the results when the training data was augmented by the random-positions-in-sphere data. Similar plots for all other isomers are shown in the Supplementary Online Information.
• Figure 5: Initial (blue) and predicted (orange) position distributions for all atoms of the eight tested isomers, shown in the same order as in Fig. \ref{['fig:results']} of the main text. In panel (d), the red lines show the results when the training data was augmented by the random-positions-in-sphere data.