Born-Oppenheimer approximation for a harmonic molecule

TL;DR

This paper investigates the application of the Born-Oppenheimer approximation to a harmonic diatomic molecule with one electron, comparing exact and approximate results for internal and center-of-mass motions, and discussing symmetry and limitations.

Contribution

It provides a detailed analysis of the Born-Oppenheimer approximation's accuracy for a harmonic molecule, including symmetry considerations and potential applications.

Findings

Approximate results closely match exact solutions for internal degrees of freedom.

The approximation's validity extends to center-of-mass motion under certain conditions.

Discussion of permutation symmetry impacts on the approximation.

Abstract

We apply the Born--Oppenheimer approximation to a harmonic diatomic molecule with one electron. We compare the exact and approximate results not only for the internal degrees of freedom but also for the motion of the center of mass. We address the problem of the permutation symmetry of identical nuclei and discuss other applications of the model and its limitations.