Competing Ionization and Dissociation: Extension of the energy-dependent frame transformation to the gerade symmetry of H$_2$

TL;DR

This paper extends the energy-dependent frame transformation method to handle multiple low-energy potential curves and dissociation channels in electron collisions with H₂ cation, enabling more accurate modeling of ionization and dissociation processes.

Contribution

It introduces a generalized EDFT approach for molecules with multiple potential curves and provides a method to extract dissociation channels, validated against exact solutions for H₂.

Findings

Accurately maps fixed-nuclei scattering matrices to lab frame including dissociation.

Extends EDFT to molecules with multiple low-energy potential curves.

Demonstrates effectiveness through benchmark against H₂ model.

Abstract

This article solves two major tasks that frequently arise in the theory of electron collisions with a target molecular cation. First, it extends the energy-dependent frame transformation treatment(EDFT), which is needed to map fixed-nuclei electron-molecule scattering matrices into an energy-dependent laboratory frame scattering matrix with vibrational channel indices. The EDFT mapping can now be carried out even when the target molecule possesses multiple low energy potential curves, significantly transcending previous applications. Secondly, it implements a method to extract the rest of the full lab-frame scattering matrix, i.e. the columns and rows describing input and/or output dissociation channels. The treatment is benchmarked in this article against the essentially exact solution of a refined two-dimensional model of the singlet gerade $\Sigma$ symmetry of H$_2$. Our tests demonstrate that the theory accurately maps fixed-nuclei scattering information, of the type provided by existing electron-molecule computer codes, into a laboratory-frame scattering matrix that includes both ionization and dissociation. This treatment can provide a general framework applicable to a broad class of electron collision processes involving diatomic target ions, suitable for an accurate description of challenging processes such as dissociative recombination.