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 Møller–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, κ-OOMP2 was shown
to address the energy divergence issue in, for example, bond-breaking
processes while offering a significant improvement in accuracy for
the W4-11 thermochemistry data set, and a parameter of κ = 1.45
was recommended. A more recent investigation of regularized MP2 with
Hartree–Fock orbitals revealed that stronger regularization
(i.e., smaller values of κ) than what had previously been recommended
for κ-OOMP2 may offer huge improvements in certain cases such
as noncovalent interactions while retaining a high level of accuracy
for main-group thermochemistry data sets. In this study, we investigate
the transferability of those findings to κ-OOMP2 and assess
the implications of stronger regularization on the ability of κ-OOMP2
to diagnose strong static correlation. We found similar results using
κ-OOMP2 for several main-group thermochemistry, barrier height,
and noncovalent interaction data sets including both closed shell
and open shell species. However, stronger regularization yielded substantially
higher accuracy for open-shell transition-metal (TM) thermochemistry
and is necessary to provide qualitatively correct spin symmetry breaking
behavior for several large and electrochemically relevant TM systems.
We therefore find a single κ value insufficient to treat all
systems using κ-OOMP2.