Short-range stabilizing potential for computing energies and lifetimes of temporary anions with extrapolation methods

Abstract

The energy of a temporary anion can be computed by adding a stabilizing potential to the molecular Hamiltonian, increasing the stabilization until the temporary state is turned into a bound state, and then further increasing the stabilization until enough bound state energies have been collected so that these can be extrapolated back to vanishing stabilization. The lifetime can be obtained from the same data, but only if the extrapolation is done through analytic continuation of the momentum as a function of the square root of a shifted stabilizing parameter. This method is known as analytic continuation of the coupling constant, and it requires--at least in principle--that the bound-state input data are computed with a short-range stabilizing potential. In the context of molecules and ab initio packages, long-range Coulomb stabilizing potentials are, however, far more convenient and have been used in the past with some success, although the error introduced by the long-rang nature of the stabilizing potential remains unknown. Here, we introduce a soft-Voronoi box potential that can serve as a short-range stabilizing potential. The difference between a Coulomb and the new stabilization is analyzed in detail for a one-dimensional model system as well as for the (2)Πu resonance of CO2(-), and in both cases, the extrapolation results are compared to independently computed resonance parameters, from complex scaling for the model, and from complex absorbing potential calculations for CO2(-). It is important to emphasize that for both the model and for CO2(-), all three sets of results have, respectively, been obtained with the same electronic structure method and basis set so that the theoretical description of the continuum can be directly compared. The new soft-Voronoi-box-based extrapolation is then used to study the influence of the size of diffuse and the valence basis sets on the computed resonance parameters.

Projected CAP/SAC‐CI method with smooth Voronoi potential for calculating resonance states

“…In this work, we use a newly introduced smooth Voronoi‐CAP which wraps around the molecule like a van der Waals cavity [see eqs. (8) and below] . The resonance energy, E res , is then obtained from one of the ‐trajectories of the eigenvalues of .…”

“…In general, because of these issues, the usage of the method has been limited to small or highly symmetric molecules so far. One step to less symmetric molecules is so‐called “Voronoi potential,” which wraps around the molecule similar to a van der Waals surface. We have also performed benchmarks of this potential comparing with the performance of the soft box potential for small molecules and their related interacting systems…”

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

“…29 but is identical to the potential used in other studies. 22,23,28 Second we consider an attractive Gaussian potential of the form…”

“…25,[27][28][29][30] In most of these studies, a Coulomb potential is used to bind the resonance as in the method of scaled nuclear charges. The exception is the manifestly short-range Voronoi potential suggested by Sommerfeld et al 28 Sommerfeld and coworkers noted that the long-range Coulomb potential is not formally applicable and obtained much more consistent results with their Voronoi potential. Despite this fact, methods employing a Coulomb potential have had moderate success with shape resonances in polyatomic molecules.…”

Shape and core‐excited resonances of thionucleobases

“…TASs can be characterized by several different computational approaches, such as SM, complex scaling and complex absorbing potential techniques, and scattering calculations . SM has many variants . In this study, the orbital exponents in diffuse basis functions will be scaled and it is denoted as the exponent SM method .…”