Exterior Complex Scaling Approach for Atoms and Molecules in Strong DC Fields

TL;DR

This paper reviews the exterior complex scaling method for calculating resonance parameters in atoms and molecules under strong DC fields, demonstrating its effectiveness through various atomic and molecular examples.

Contribution

It introduces a numerical implementation of exterior complex scaling for resonance calculations in atoms and molecules, validating the approach with multiple systems and comparing to existing literature.

Findings

Resonance parameters for hydrogen in a DC field match literature values.

Widths for water molecule valence orbitals agree with coupled-cluster methods.

Method shows independence from the scaling angle in numerical results.

Abstract

We perform a short review of the history of quantum mechanics, with a focus on the historical problems with describing ionization theoretically in the context of quantum mechanics. The essentials of the theory of resonances are presented. The exterior complex scaling method for obtaining resonance parameters within the context of the Schrodinger equation is detailed. We explain how this is implemented for a numerical solution using a finite element method for the scaled variable. Results for the resonance parameters of a one-dimensional hydrogen model in an external direct current (DC) electric field are presented as proof of the independence of the theory from the scaling angle. We apply the theory to the real hydrogen atom in a DC field and present results which agree with literature values. The resonance parameters for singly ionized helium are also presented. Using a model potential energy for the water molecule, we solve for the energy eigenvalues. We then solve for the resonance parameters of the water molecule in a DC field and compare to literature results. Our widths for the valence orbital are shown to agree well with the so-called "coupled-cluster singles and doubles with perturbative triples excitations" method.