Electronic quantum trajectories with quantum nuclei

TL;DR

This paper extends quantum trajectory methods to include fully quantum-mechanical nuclei using the exact factorization approach, enabling more accurate simulations of electron dynamics in molecular systems beyond the Born-Oppenheimer approximation.

Contribution

It introduces a fully quantum-mechanical framework for electronic trajectories that incorporates quantum nuclear effects, overcoming limitations of traditional methods.

Findings

Developed a quantum clock-dependent quantum hydrodynamics theory.

Demonstrated electronic trajectories for quantum nuclei in a proton-coupled electron transfer model.

Laid groundwork for trajectory-based electron dynamics simulations beyond BOA.

Abstract

Quantum trajectory calculations for electrons are a useful tool in the field of molecular dynamics, e.g. to understand processes in ultrafast spectroscopy. They have, however, two limitation: On the one hand, such calculations are typically based on the Born-Oppenheimer approximation (BOA) and the electron dynamics for stationary nuclei is considered, thus neglecting quantum effects of the nuclei. On the other hand, even if the quantum nuclear motion would be taken into account, a BOA dynamics on a single potential energy surface would not provide any electron trajectories because the electronic part is treated as a stationary problem. By using the exact factorization method, we overcome these limitations and generalize the theory of electronic quantum trajectories to a fully quantum-mechanical treatment of the nuclei. After reviewing the time-dependent theory of quantum hydrodynamics and quantum trajectories, we show that the nuclei can be viewed as a quantum clock for the electronic motion and we develop a fully quantum-mechanical clock-dependent version of quantum hydrodynamics. This theory is used to obtain electronic trajectories for quantum nuclei, as is exemplified for a model system of a proton-coupled electron transfer dynamics. Our work generalizes the concept of quantum trajectories and lays the foundations for the development of trajectory-based simulation methods of electron dynamics beyond the BOA.