Connections and performances of Green's function methods for charged and neutral excitations

TL;DR

This paper explores the connections and performance of Green's function methods, especially the GW approximation and Bethe-Salpeter equation, for charged and neutral excitations, including a case study on cycl[3,3,3]azine.

Contribution

It analyzes the relationships between Green's function methods and evaluates their effectiveness, highlighting the need for dynamical corrections in BSE to predict specific molecular properties.

Findings

GW approximation accurately predicts ionization potentials.

Second-order BSE with dynamical correction is essential for inverted singlet-triplet gaps.

Green's function methods outperform some wave function approaches in certain excitations.

Abstract

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established $GW$ approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe-Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely-known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the $GW$ approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic.