Complex Absorbing Potential Green's Function Methods for Resonances

The complex absorbing potential (CAP) formalism has been successfully employed in various wave function-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, despite a few influential contributions, have seen only 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 N₂^-, CO^-, CO₂^-, C₂H₂^-, C₂H₄^-, and 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 wave function-based methods.