Exact factorization of the time-dependent electron-nuclear wavefunction

TL;DR

This paper introduces an exact method to decompose the combined electron-nuclear wavefunction in time-dependent systems, providing new insights into molecular dissociation mechanisms via a rigorously defined potential energy surface.

Contribution

It derives formally exact equations for electron and nuclear wavefunctions, defining a time-dependent potential energy surface and geometric phase, with applications to molecular dissociation.

Findings

TDPES helps identify dissociation mechanisms in H2+

Provides a rigorous framework for electron-nuclear wavefunction decomposition

Enhances interpretive tools for time-dependent molecular dynamics

Abstract

We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the $H_2^+$ molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.