We discuss the analytic and diagrammatic structure of ionization potential (IP) and electron affinity (EA) equation-ofmotion 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 ringladder 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 GW100 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. EOM GW EO EOM-CCSDT EOM-CCSD GW Number of diagrams included in the one-particle Green's functionTable of contents figure.Within the molecular physics and quantum chemistry communities, a number of perturbative schemes have been proposed to directly construct the self-energy, 12,13 including the outer-valence Green's function approach, 12 the two-particlehole Tamm-Dancoff approximation 14 and its extended variant, 15 and the algebraic diagrammatic construction. 16 More recently the second-order Green's function 17,18 has been studied, especially in its self-consistent 19 and finite-temperature 20 variations. In wavefunction-based techniques, ionization potentials and electron affinities can either be calculated as a difference in ground-state energies (between the neutral and ionic systems) or via the equation-of-motion framework, which directly results in an eigensystem whose eigen-arXiv:1805.00043v1 [physics.chem-ph]