Connection between GW and Extended Coupled Cluster

Area of Science:

• Quantum chemistry
• Theoretical physics
• Computational chemistry

Background:

• Coupled-cluster (CC) theory and Green's function many-body perturbation theory (MBPT) are distinct frameworks for electronic correlation.
• CC methods use exponential wave function parametrizations for size extensivity.
• Green's function methods like GW approximation describe excitations via diagrammatic resummations.

Purpose of the Study:

• Establish a formal correspondence between CC and Green's function theories.
• Introduce the extended CC (ECC) ansatz as a unified framework.
• Explore novel avenues for incorporating vertex corrections within CC.

Main Methods:

• Formal analysis establishing the equivalence between GW approximation and equation-of-motion (EOM) treatment of direct-ring CC doubles (drCCD).
• Development and application of the extended CC (ECC) ansatz.
• Investigation of Green's function properties within the ECC framework.

Main Results:

• Demonstrated formal equivalence between the GW approximation and EOM-drCCD.
• The ECC ansatz provides a unified framework connecting CC and MBPT.
• ECC facilitates the incorporation of vertex corrections into CC theory.

Conclusions:

• The ECC ansatz bridges CC and Green's function methods.
• This unified framework offers systematic improvability for Green's function approaches.
• ECC preserves a sum-over-state representation of the self-energy.