Eur. Phys. J. D (2021) 75: 316
https://doi.org/10.1140/epjd/s10053-021-00332-z

Regular Article – Atomic and Molecular Collisions

Computing resonance energies directly: method comparison for a model potential

Department of Chemistry and Physics, Southeast Louisiana University, SLU 10878, 70402, Hammond, LA, USA

^b thomas.sommerfeld@selu.edu

Received: 18 October 2021
Accepted: 15 December 2021
Published online: 30 December 2021

Abstract

In contrast to bound states, electronically metastable states or resonances still represent a major challenge for quantum chemistry and molecular physics. The reason lies in the embedding continuum: Bound states represent a many-body problem, while resonances represent a simultaneous scattering and many-body problem. Here we focus on so-called ${\mathcal{L}}^2$-methods, which treat the continuum only implicitly, but rather take the ‘decaying state’ perspective and emphasize electron correlation in the decaying state. These methods represent a natural extension of quantum chemistry into the metastable domain and are suitable for, say, modeling electron-induced reactions or resonant photo detachment. The three workhorse ${\mathcal{L}}^2$-methods are complex absorbing potentials, the stabilization method, and regularized analytic continuation. However, even for these three methods, making comparisons is less than straightforward as each method works best with a unique blend of electronic structure methods and basis sets. Here we address this issue by considering a model potential. For a model, we can establish a reliable reference resonance energy by using the complex scaling method and a discrete variable representation. Then, we can study the performance of the three workhorse methods as well as effects of more approximate Gaussian basis sets.