On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation

TL;DR

This paper compares the diagrammatic structures of equation-of-motion coupled-cluster (EOM-CC) theory and the GW approximation, revealing how EOM-CC includes various diagrams and vertex corrections, and presents numerical results on molecular ionization energies.

Contribution

It provides a detailed diagrammatic comparison between EOM-CC and GW, showing how higher excitations in EOM-CC encompass GW diagrams and vertex corrections.

Findings

EOM-CCSD includes fewer ring diagrams than GW due to time-ordering.

EOM-CCSDT includes all GW diagrams plus additional vertex corrections.

Numerical results highlight the importance of exchange and screening in molecular ionization energies.

Abstract

We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-of-motion coupled-cluster (EOM-CC) theory, in order to put it on equal footing with the prevalent $GW$ approximation. The comparison is most straightforward for the time-ordered one-particle Green's function, and we show that the Green's function calculated by EOM-CC with single and double excitations (EOM-CCSD) includes fewer ring diagrams at higher order than does the $GW$ approximation, due to the former's unbalanced treatment of time-ordering. However, the EOM-CCSD Green's function contains a large number of vertex corrections, including ladder diagrams, mixed ring-ladder diagrams, and exchange diagrams. By including triple excitations, the EOM-CCSDT Green's function includes all diagrams contained in the $GW$ approximation, along with many high-order vertex corrections. In the same language, we discuss a number of common approximations to the EOM-CCSD equations, many of which can be classified as elimination of diagrams. Finally, we present numerical results by calculating the principal charged excitations energies of the molecules contained in the so-called $GW$100 test set [J. Chem. Theory Comput. 2015, 11, 5665-5687]. We argue that (in molecules) exchange is as important as screening, advocating for a Hartree-Fock reference and second-order exchange in the self-energy.