Low-energy Electron collisions with O$_2$: Test of Molecular R-matrix without Diagonalization

TL;DR

This study investigates low-energy electron collisions with O₂ molecules using an ab initio R-matrix method, comparing models and introducing a diagonalization-free approach suitable for large Hamiltonians.

Contribution

It introduces a linear equation solver approach for R-matrix calculations that avoids diagonalization, enabling analysis of larger systems with improved physical accuracy.

Findings

Anionic molecular orbital models match experimental results well.

The diagonalization-free method effectively computes scattering parameters.

Different target models impact the accuracy of scattering eigenphases.

Abstract

Electron collisions with O$_2$ at scattering energies below 1 eV are studied in the fixed-nuclei approximation for a range of internuclear separations using the ab initio molecular R-matrix method. The $^2\Pi_g$ scattering eigenphases and quantum defects are calculated. The parameters of the resonance and the energy of the bound negative ion are then extracted. Different models of the target that employ molecular orbitals calculated for the neutral target are compared with models based on anionic orbitals. A model using a basis of anionic molecular orbitals yields physically correct results in good agreement with experiment. An alternative method of calculation of the R-matrix is tested, where instead of performing a single complete diagonalization of the Hamiltonian matrix in the inner region, the system of linear equations is solved individually for every scattering energy. This approach is designed to handle problems where diagonalization of an extremely large Hamiltonian is numerically too demanding.