As a first model system we consider the homogeneous electron gas (HEG), which plays a central role in understanding the properties of simple metals and is of essential importance to the foundations of density functional theory. The divergence of second-order perturbation theory for the infinite HEG has long been proven analytically. More recently, finite periodic electron gases have emerged as important numerical benchmark systems for many-body theories. Importantly, this showed that MP2 also diverges for these systems, even though they display significant energy gaps. Since the divergence of canonical MP2 for the HEG is thus well established, it is of particular interest to understand how the regularized methods behave in comparison. In Fig. , the per electron correlation energies of κ-MP2 and xBW2 are plotted against the corresponding MP2 values. Here, each point corresponds to an electron gas with N e =14 -FIG. . Correlation energies per electron of different electronic structure methods plotted against the MP2 correlation energy per electron. Deviation from linearity in this plot indicates convergence or slower divergence than MP2. Data for mCCD and RPA+SOSEX are taken from reference [20].