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

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.

References in corpus (11)

• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Coupled cluster theory in materials science
• Full-Frequency GW without Frequency
• All-electron Gaussian-based $G_0{W}_0$ for Valence and Core Excitation Energies of Periodic Systems
• A periodic equation-of-motion coupled-cluster implementation applied to $F$-centers in alkaline earth oxides
• Connections between many-body perturbation and coupled-cluster theories
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory
• Improving MP2 band gaps with low-scaling approximations to EOM-CCSD
• Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids

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