Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction

TL;DR

This paper presents an exact factorization approach for the coupled electron-nuclear wavefunction, introducing a time-dependent potential energy surface that enhances understanding of molecular dynamics beyond traditional methods.

Contribution

It provides a detailed derivation of the exact factorization formalism and demonstrates its application to interpret electron-nuclear dynamics in a model molecule.

Findings

Exact TDPES reveals dissociation mechanisms.

Comparison shows differences from traditional potential energy surfaces.

Ehrenfest dynamics on TDPES offers improved insights.

Abstract

It was recently shown [Phys. Rev. Lett. 105, 123002 (2010)] that the complete wavefunction for a system of electrons and nuclei evolving in a time-dependent external potential can be exactly factorized into an electronic wavefunction and a nuclear wavefunction. The concepts of an exact time-dependent potential energy surface (TDPES) and exact time-dependent vector potential emerge naturally from the formalism. Here we present a detailed description of the formalism, including a full derivation of the equations that the electronic and nuclear wavefunctions satisfy. We demonstrate the relationship of this exact factorization to the traditional Born-Oppenheimer expansion. A one-dimensional model of the H$_2^+$ molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: we show how features of its structure indicate the mechanism of dissociation. We compare the exact TDPES with potential energy surfaces from the time-dependent Hartree-approach, and also compare traditional Ehrenfest dynamics with Ehrenfest dynamics on the exact TDPES.