We have been investigating the combination of a short-range density functional approximation with long-range random phase approximation (RPA) correlation, where the direct RPA correlation is constructed using only Coulomb (i.e., not antisymmetrized) two-electron integrals. Our group’s recently demonstrated connection between RPA and coupled cluster theory suggests investigating a related method: second-order Møller–Plesset perturbation theory correlation (MP2) constructed using only Coulomb integrals. This new “JMP2” method is related to the scaled-opposite-spin SOS-MP2 approximation [Y. Jung, R. C. Lochan, A. D. Dutoi and M. Head-Gordon, J. Chem. Phys., 2004, 121, 9793], which is also constructed using only Coulomb integrals. While JMP2 and SOS-MP2 yield identical results for closed shell systems, they have important differences for open shells. We show here that both JMP2 and SOS-MP2 provide a reasonable treatment of long-range correlation when combined with a short-range exchange–correlation functional. Remarkably, JMP2’s explicit inclusion of (approximate) like-spin correlation effects provides significant improvements over SOS-MP2 for thermochemistry.