Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism

TL;DR

This paper establishes exact theoretical relationships between the GW approximation and equation-of-motion coupled-cluster theories, providing insights into their equivalences and differences through the quasi-boson formalism, supported by numerical demonstrations.

Contribution

It reveals the exact connections between GW and EOM-CC theories, clarifies the role of screening approximations, and introduces particle-hole decoupling approaches within this framework.

Findings

Exact equivalence of G0W0 and electron-boson propagator theory.

Analysis of screening limitations in IP+EA-EOM-CC and G0W0 Tamm-Dancoff.

Numerical validation of theoretical relationships on molecular ionization potentials.

Abstract

We describe the relationship between the GW approximation and various equation-of-motion (EOM) coupled-cluster (CC) theories. We demonstrate the exact equivalence of the G$_0$W$_0$ approximation and the propagator theory for an electron-boson problem in a particular excitation basis. From there, we establish equivalence within the quasi-boson picture to the IP+EA-EOM unitary coupled-cluster propagator. We analyze the incomplete description of screening provided by the standard similarity-transformed IP+EA-EOM-CC and the recently introduced G$_0$W$_0$ Tamm-Dancoff approximation. We further consider the approximate decoupling of IP and EA sectors in EOM-CC treatments and devise the analogous particle-hole decoupling approach for the G$_0$W$_0$ approximation. Finally, we numerically demonstrate the exact relationships and magnitude of the approximations in calculations of a set of molecular ionization potentials and electron affinities.