Variational solutions for Resonances by a Finite-Difference Grid Method

TL;DR

This paper introduces a modified finite difference grid method that satisfies the variational principle, enabling accurate calculation of both real and complex resonances in molecular and nuclear systems.

Contribution

The authors adapt the finite difference grid method to incorporate the variational principle for calculating resonances, including complex poles of the scattering matrix.

Findings

Allows calculation of electronic autoionization resonances.

Enables study of nuclear predissociation resonances.

Provides energies and lifetimes of metastable states.

Abstract

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as resonances and provide the energies and inverse lifetimes of the system under study (e.g., molecules) in metastable states. This approach allows incorporating finite grid methods in the study of resonance phenomena in chemistry. Possible applications include the calculation of electronic autoionization resonances which occur when ionization takes place as the bond lengths of the molecule are varied. Alternatively, the method can be applied to calculate nuclear predissociation resonances which are associated with activated complexes with finite lifetimes.