Improving MP2 bandgaps with low-scaling approximations to EOM-CCSD

Despite its reasonable accuracy for ground-state properties of semiconductors and insulators, second-order Møller-Plesset perturbation theory (MP2) significantly underestimates bandgaps. In this work, we evaluate the bandgap predictions of partitioned equation-of-motion MP2 (P-EOM-MP2), which is a second-order approximation to EOM 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 bandgaps 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 Perdew-Burke-Ernzerhof 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.