Dissociative recombination by frame transformation to Siegert pseudostates: A~comparison with a numerically solvable model

TL;DR

This paper introduces a high-precision two-dimensional model for dissociative recombination, comparing an exact numerical solution with an approximate method using Siegert pseudostates to evaluate their accuracy.

Contribution

It provides a benchmark for dissociative recombination calculations by comparing an exact model with an approximate frame transformation approach using Siegert pseudostates.

Findings

The exact model yields highly precise results without approximations.

The approximate method with Siegert pseudostates closely matches the exact results.

The comparison validates the use of Siegert pseudostates in modeling dissociative recombination.

Abstract

We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H$_2^+$ and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multi-channel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.