On the relation between the GW approximation and (Unitary) Coupled Cluster theory

The first formal connection between the particle-hole (ph) random phase approximation (RPA) and the so-called ring-Coupled Cluster (CC) formalism has been established by Scuseria et al. in 2008.¹

However, until now a formal connection between the GW approximation, which is commonly based on the phRPA for the screened Coulomb interaction, and Coupled Cluster theory has not been established.

Besides being interesting from a purely theoretical point of view, the connection also enhances the understanding of the advantages and disadvantages of the individual methods.

In this contribution, we demonstrate the formal connection between the two theories.

As a result, we can reveal the origin of missing phRPA screening in the similarity transformed equation of motion CC singles and doubles method for the determination of quasi-particles.

Additionally, the analysis reveals possible routes to decrease the starting point dependence of G₀W₀ and to find systematic improvements upon the GW approximation.

1) G. E. Scuseria, T. M. Henderson, and D. C. Sorensen, J. Chem. Phys. 129, 231101 (2008)