An analogous plot is shown for κ-MP2 in Fig. . As the Hubbard model Hamiltonian uses an arbitrary energy scale given by the hopping parameter t, there is no meaningful way to translate the empirically optimized value of κ to this system. We therefore consider a range of regularization strengths. For κ → ∞, the original diverging MP2 curve is recovered, while for κ → 0, the restricted Hartree-Fock (RHF) curve is obtained, as the correlation energy contribution vanishes. Taking these limits of κ into account, several intermediate values were considered, so that the regularized calculations repro- duced the FCI energy at the correlation strengths U/t = 8, 13, 18, respectively. Interestingly, none of these methods outperforms xBW2, despite the fact that they were explicitly fitted to the FCI results. Indeed, all κ-MP2 curves display significant curvature, so that they are either over-or underregularized in some range and ultimately diverge. Graphene-Water Interaction: Finally, we test the regularized methods for the interaction of graphene with a single water molecule. This system has been intensively studied as a highly challenging benchmark for many-body methods. As a case in point, MP2 significantly overestimates this interaction, as is commonly observed for non-covalent interactions involving large, polarizable systems. Consequently, only computationally demanding many-body treatments at the CCSD(T) or QMC level offer predictive accuracy on this system.