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Computing resonance energies directly: method comparison for a model potential

  • Regular Article – Atomic and Molecular Collisions
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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.

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“This manuscript has data included as electronic supplementary material”.

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Acknowledgements

Support from the National Science Foundation under Grant No. 1856775 is gratefully acknowledged.

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Authors and Affiliations

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

    Jeremy U. Davis Jr. & Thomas Sommerfeld

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  1. Jeremy U. Davis Jr.
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  2. Thomas Sommerfeld
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All authors contributed equally to the paper.

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Correspondence to Thomas Sommerfeld.

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Davis, J.U., Sommerfeld, T. Computing resonance energies directly: method comparison for a model potential. Eur. Phys. J. D 75, 316 (2021). https://doi.org/10.1140/epjd/s10053-021-00332-z

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00332-z

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