Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes

TL;DR

This paper investigates the electron-nuclear coupling operator within the exact factorization framework, proposing a semiclassical approximation method to better understand non-adiabatic processes in quantum dynamics.

Contribution

It introduces a numerical procedure to approximate the electron-nuclear coupling operator using semiclassical nuclear dynamics, advancing the analysis of non-adiabatic effects.

Findings

Developed a semiclassical approximation method for the coupling operator

Enhanced understanding of non-adiabatic electron-nuclear interactions

Provided a numerical approach applicable to complex quantum systems

Abstract

In the context of the exact factorization of the electron-nuclear wave function, the coupling between electrons and nuclei beyond the adiabatic regime is encoded (i) in the time-dependent vector and scalar potentials and (ii) in the electron-nuclear coupling operator. The former appear in the Schroedinger-like equation that drives the evolution of the nuclear degrees of freedom, whereas the latter is responsible for inducing non-adiabatic effects in the electronic evolution equation. As we have devoted previous studies to the analysis of the vector and scalar potentials, in this paper we focus on the properties of the electron-nuclear coupling operator, with the aim of describing a numerical procedure to approximate it within a semiclassical treatment of the nuclear dynamics.