On the validity of the Born-Oppenheimer approximation in the indirect dissociative recombination process

TL;DR

This paper introduces a two-dimensional R-matrix method to analyze vibrational excitation and dissociation in electron-molecule collisions, assessing the validity of the Born-Oppenheimer approximation in dissociative recombination.

Contribution

It develops a novel 2D R-matrix approach for simple models of electron-molecule interactions, providing benchmarks for Born-Oppenheimer approximation accuracy.

Findings

The 2D R-matrix method accurately models dissociative recombination.

Born-Oppenheimer approximation shows limitations in describing the process.

First-order nonadiabatic corrections improve approximation accuracy.

Abstract

An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of freedom. The two-dimensional $R$-matrix can be constructed simultaneously on the electronic and nuclear surfaces using all three forms developed previously for electron-atom and electron-molecule collisions. These are the eigenchannel $R$-matrix form, inversion technique of Nesbet and Robicheaux, and the Wigner-Eisenbud-type form using expansion over the poles of the symmetrized Hamiltonian. The 2D $R$-matrix method is employed to solve a simple model tailored to describe the dissociative recombination and the vibrational excitation of H$_2^+$ cation in the singlet ungerade symmetry $^1\Sigma_u$. These results then serve as a (near-exact) benchmark for the following calculation in which the $R$-matrix states are replaced by their Born-Oppenheimer approximations. The accuracy of this approach and its correction with the first-order nonadiabatic couplings are discussed.