Optimizing the Regularization in Size-Consistent Second-Order Brillouin-Wigner Perturbation Theory

Despite its simplicity and relatively low computational cost, second-order M{\o}ller-Plesset perturbation theory (MP2) is well-known to overbind noncovalent interactions between polarizable monomers and some organometallic bonds. In such situations, the pairwise-additive correlation energy expression in MP2 is inadequate. Although energy-gap dependent amplitude regularization can substantially improve the accuracy of conventional MP2 in these regimes, the same regularization parameter worsens the accuracy for small molecule thermochemistry and density-dependent properties. Recently, we proposed a repartitioning of Brillouin-Wigner perturbation theory that is size-consistent to second order (BW-s2), and a free parameter ({\alpha}) was set to recover the exact dissociation limit of H$_2$ in a minimal basis set. Alternatively {\alpha} can be viewed as a regularization parameter, where each value of {\alpha} represents a valid variant of BW-s2, which we denote as BW-s2({\alpha}). In this work, we semi-empirically optimize {\alpha} for noncovalent interactions, thermochemistry, alkane conformational energies, electronic response properties, and transition metal datasets, leading to improvements in accuracy relative to the ab initio parameterization of BW-s2 and MP2. We demonstrate that the optimal {\alpha} parameter ({\alpha} = 4) is more transferable across chemical problems than energy-gap-dependent regularization parameters. This is attributable to the fact that the BW-s2({\alpha}) regularization strength depends on all of the information encoded in the t amplitudes rather than just orbital energy differences. While the computational scaling of BW-s2({\alpha}) is iterative $\mathcal{O}(N^5)$, this effective and transferable approach to amplitude regularization is a promising route to incorporate higher-order correlation effects at second-order cost.