Retrieval of the nuclear motion in a molecule from photoelectron momentum distributions using non-Born-Oppenheimer quantum dynamics and deep learning

TL;DR

This paper demonstrates that deep learning models can accurately extract the time-dependent bond length and electronic properties of a molecule from photoelectron momentum distributions, based on non-Born-Oppenheimer quantum dynamics simulations.

Contribution

It introduces a neural network approach trained on non-Born-Oppenheimer quantum dynamics data to retrieve molecular bond lengths from photoelectron momentum distributions.

Findings

Neural network retrieves bond length with 0.2-0.4 a.u. error.

Method works for molecules in excited and ground states.

Potential for extracting electronic properties from electron momentum data.

Abstract

By using a neural network that takes momentum distributions of photoelectrons produced in strong-field ionization as input, we retrieve the time-dependent bond length of a dissociating one-dimensional H$_{2}^{+}$ molecule. The photoelectron momentum distributions are calculated from the direct numerical solution of the non-Born-Oppenheimer time-dependent Schr\"{o}dinger equation. We simulate two setups: first, molecules prepared in the first excited electronic state, second, a pump-probe scheme starting from the ground state. We show that in both schemes a neural network trained on momentum distributions calculated for frozen nuclei retrieves the time-dependent bond length with an absolute error of $0.2$-$0.4$ a.u. We find that a neural network, when applied to photoelectron momentum distributions obtained within the pump-probe scheme, can be used for the retrieval of the equilibrium internuclear distance and ground-state population. This opens new perspectives for extracting electronic properties of molecules from electron momentum distributions using deep learning.