On Corrections to the Born-Oppenheimer Approximation

TL;DR

This paper introduces a novel perturbation theory-based approach to improve the treatment of electron-nuclear coupling in quantum molecular calculations, extending the Born-Oppenheimer approximation to include both adiabatic and non-adiabatic effects.

Contribution

It presents a new methodology that generalizes the Born-Oppenheimer approximation by incorporating both adiabatic and non-adiabatic corrections through perturbation theory.

Findings

The method includes all adiabatic terms without explicit nuclear wavefunctions.

Non-adiabatic corrections enable nuclei to move on multiple potential surfaces.

A simple example demonstrates the technique's mechanics.

Abstract

This report presents a new approach for treating the coupling of electrons and nuclei in quantum mechanical calculations for molecules and condensed matter. It includes the standard "Born-Oppenheimer approximation" as a special case but treats both adiabatic and non-adiabatic corrections using perturbation theory. The adiabatic corrections include all terms that do not explicitly involve the nuclear wavefunctions, so that the nuclei move on a single electronic potential surface. The non-adiabatic corrections, which allow the nuclei to move on more than one potential surface, include coupling between the electronic and nuclear wavefunctions. The method is related to an approach first proposed by Born and Huang, but it differs in the methodology and in the definition of the electronic wavefunctions and potential surfaces. A simple example is worked out to illustrate the mechanics of the technique. The report also includes a review of previous work.