Revisiting the Orbital Energy Dependent Regularization of Orbital Optimized Second Order Møller-Plesset Theory

Optimizing orbitals in the presence of electron correlation, as in orbital optimized second-order M{\o}ller-Plesset perturbation theory (OOMP2), can remove artifacts associated with mean-field orbitals such as spin contamination and artificial symmetry-breaking. However, OOMP2 is known to suffer from divergent correlation energies in regimes of small orbital energy gaps. To address this issue, several approaches to amplitude regularization have been explored, with those featuring energy-gap dependent regularizers appearing to be most transferable and physically justifiable. For instance, $\kappa$-OOMP2 was shown to address the energy divergence issue in, e.g., bond-breaking processes while offering a significant improvement in accuracy for the W4-11 thermochemistry dataset, and a parameter of $\kappa$=1.45 was recommended. A more recent investigation of regularized MP2 with Hartree-Fock orbitals revealed that stronger regularization (i.e. smaller values of $\kappa$) than what had previously been recommended for $\kappa$-OOMP2 may offer huge improvements in certain cases such as noncovalent interactions while retaining a high level of accuracy for main-group thermochemistry datasets. In this study we investigate the transferability of those findings to $\kappa$-OOMP2 and assess the implications of stronger regularization on the ability of $\kappa$-OOMP2 to diagnose strong static correlation. We found similar results using $\kappa$-OOMP2 for several main-group thermochemistry, barrier height, and noncovalent interaction datasets including both closed shell and open shell species. However, stronger regularization yielded substantially higher accuracy for open-shell transition metal thermochemistry, and is necessary to provide qualitatively correct spin symmetry breaking behavior for several large and electrochemically-relevant transition metal systems. We therefore find a single $\kappa$ value insufficient to treat all systems using $\kappa$-OOMP2.