On the status of the Born-Oppenheimer expansion in molecular systems theory

TL;DR

The paper critiques the limitations of the traditional Born-Oppenheimer expansion in molecular systems, demonstrating its inapplicability in certain cases and proposing a new perturbation theory approach.

Contribution

It reveals fundamental issues with the Born-Oppenheimer expansion and introduces a novel perturbation theory tailored for molecular systems.

Findings

Born-Oppenheimer expansion fails necessary perturbation conditions

An exact solution example shows limitations of the traditional approach

A new perturbation theory framework is proposed

Abstract

It is shown that the adiabatic Born-Oppenheimer expansion does not satisfy the necessary condition for the applicability of perturbation theory. A simple example of an exact solution of a problem that can not be obtained from the Born-Oppenheimer expansion is given. A new version of perturbation theory for molecular systems is proposed.