Complex Absorbing Potential Green's Function Methods for Resonances

TL;DR

This paper introduces a novel Green's function approach incorporating complex absorbing potentials (CAP) within the GW approximation to accurately describe electronic resonances, validated on several molecular anions.

Contribution

It integrates CAP formalism into the GW method, enabling efficient and accurate computation of resonance energies and lifetimes within a Green's function framework.

Findings

Accurately predicts resonance positions and lifetimes for various molecular anions.

Achieves accuracy comparable to wavefunction-based methods.

Provides a fast, practical approach for resonance characterization.

Abstract

The complex absorbing potential (CAP) formalism has been successfully employed in various wavefunction-based methods to study electronic resonance states. In contrast, Green's function-based methods are widely used to compute ionization potentials and electron affinities but have seen limited application to resonances. We integrate the CAP formalism within the $GW$ approximation, enabling the description of electronic resonances in a Green's function framework. This approach entails a fully complex treatment of orbitals and quasiparticle energies in a non-Hermitian setting. We validate our CAP-$GW$ implementation by applying it to the prototypical shape resonances of \ce{N2^-}, \ce{CO^-}, \ce{CO_2^-}, \ce{C2H2-}, \ce{C2H4-}, and \ce{CH2O-}. It offers a fast and practical route to approximate both the lifetimes and positions of resonance states, achieving an accuracy comparable to that of state-of-the-art wavefunction-based methods.