The adiabatic limit of the exact factorization of the electron-nuclear wave function

TL;DR

This paper explores the adiabatic limit of the exact electron-nuclear wave function factorization, analyzing how non-adiabatic effects depend on nuclear mass and relate to the Born-Oppenheimer approximation, through theoretical and numerical methods.

Contribution

It introduces a new framework to study the adiabatic limit by emphasizing the mass ratio dependence in the exact factorization equations.

Findings

Non-adiabatic effects influence electronic properties.

The leading term relates to classical nuclear momentum.

Numerical tests confirm mass ratio dependence in a model system.

Abstract

We propose a procedure to analyze the relation between the exact factorization of the electron-nuclear wave function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical nuclear momentum. Its dependence on the mass ratio is tested numerically on a model proton- coupled electron transfer in different non-adiabatic regimes.