  Despite its reasonable accuracy for ground-state properties of semiconductors
and insulators, second-order Moller-Plesset perturbation theory (MP2)
significantly underestimates band gaps. Here, we evaluate the band gap
predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a
second-order approximation to equation-of-motion coupled-cluster theory with
single and double excitations. On a test set of elemental and binary
semiconductors and insulators, we find that P-EOM-MP2 overestimates band gaps
by 0.3 eV on average, which can be compared to the underestimation by 0.6 eV on
average exhibited by the G0W0 approximation with a PBE reference. We show that
P-EOM-MP2, when interpreted as a Green's function-based theory, has a
self-energy that includes all first- and second- order diagrams and a few
third-order diagrams. We find that the GW approximation performs better for
materials with small gaps and P-EOM-MP2 performs better for materials with
large gaps, which we attribute to their superior treatment of screening and
exchange, respectively.
