Analysis and Optimization of Resonance Energies and Widths Using Complex Absorbing Potentials

TL;DR

This paper introduces a new criterion, the -criterion, for optimizing complex absorbing potentials (CAPs) to accurately determine resonance energies and widths in electronic structure calculations, improving over traditional methods.

Contribution

The authors propose the -criterion for more effective CAP parameter optimization, enabling better minimization of CAP perturbations through spatial parameter trajectories.

Findings

The -criterion improves the reliability of CAP parameter optimization.

Application to dinitrogen anion demonstrates accurate resonance energy and width calculations.

Method compares two types of CAPs: box- and Voronoi-CAPs.

Abstract

Complex absorbing potentials (CAPs) are artificial potentials added to electronic Hamiltonians to make the wavefunction of metastable electronic states square-integrable. This makes the electronic structure problem of electronic resonances comparable to that of electronic bound states, thus reducing the complexity of the problem. CAPs depend on two types of parameters: the coupling parameter $\eta$ and a set of spatial parameters which define the onset of the CAP. It has been a common practice over the years to minimize the CAP perturbation on the physical electronic Hamiltonian by running an $\eta-$trajectory, whereby one fixes the spatial parameters and varies $\eta$. The optimal $\eta$ is chosen according to the minimum log-velocity criterion. But the effectiveness of an $\eta-$trajectory strongly depends on the values of the fixed spatial parameters. In this work, we propose a more general criterion, called the $\xi-$criterion, which allows one to minimize any CAP parameter, including the CAP spatial parameters. Indeed, we show that fixing $\eta$ and varying the spatial parameters according to a scheme (i.e., running a spatial trajectory) is a more efficient and reliable way of minimizing the CAP perturbations (which is assessed using the $\xi-$criterion). We illustrate the method by determining the resonance energy and width of the temporary anion of dinitrogen, at the Hartree-Fock and EOM-EA-CCSD levels, using two different types of CAPs: the box- and the smooth Voronoi-CAPs.