Computing resonance energies directly: method comparison for a model potential

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 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 L 2methods 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.

Recent Advances in the Study of Negative‐Ion Resonances Using Multiconfigurational Propagator and a Complex Absorbing Potential

“…[261] A comparative study on the performance of the CAP, stabilization and analytic continuation methods was performed by Davis and Sommerfeld. [262]…”

“…Recently, Matsika and co‐workers proposed a projected CAP in the framework of MRCI [261] . A comparative study on the performance of the CAP, stabilization and analytic continuation methods was performed by Davis and Sommerfeld [262] …”

Molecular Anions Perspective

“…Thomas Sommerfeld has introduced a so-called Voronoi potential 83 that surrounds the molecule more smoothly as illustrated in Figure 28. He has also produced a nice overview 84 of how CAP, stabilization, and other methods work by showing results for a model potential.…”

Molecular collisions, photoionization and dynamics: honouring Professor Vincent McKoy

“…For benzene, they calculated differential and integral cross sections for elastic and electronic excitation, as well as total cross sections, for electron scattering at impact energies in the 10-50 eV range. Computing resonance energies directly through a method comparison for a model potential was presented by Davis and Sommerfeld [20], Bandurin et al [21] obtained the excitation of L-valine molecules by optical spectroscopy, and new routes in the formation of positively charged fragments upon electron attachment were investigated [22]. We also note a contribution on a set of cross sections and transport coefficients for electrons in C 2 H 6 O and its mixtures with Ar and Ne [23] while Sugawara and Nakata report an analytical study on elliptic vector loci of average electron velocity of an electron swarm in constant-collision-frequency model gas under ac electric and dc magnetic fields crossed at arbitrary angles [24].…”