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We derive and assess two new classes of regularizers that cope with offendingdenominators in the single-reference second-order M{\o}ller-Plessetperturbation theory (MP2). In particular, we discuss the use of two types oforbital energy dependent regularizers, $\kappa$ and $\sigma$, in conjunctionwith orbital-optimized MP2 (OOMP2). The resulting fifth-order scaling methods,$\kappa$-OOMP2 and $\sigma$-OOMP2, have been examined for bond-breaking,thermochemistry, and biradical problems. Both methods with strong enoughregularization restore restricted to unrestricted instability (i.e.Coulson-Fischer points) that unregularized OOMP2 lacks when breaking bonds in$\text{H}_{2}$, $\text{C}_2\text{H}_6$, $\text{C}_2\text{H}_4$, and$\text{C}_2\text{H}_2$. The training of the $\kappa$ and $\sigma$regularization parameters was performed with the W4-11 set. We furtherdeveloped scaled correlation energy variants, $\kappa$-S-OOMP2 and$\sigma$-S-OOMP2, by training on the TAE140 subset of the W4-11 set. Those newOOMP2 methods were tested on the RSE43 set and the TA14 set where unmodifiedOOMP2 itself performs very well. The modifications we made were foundinsignificant in these data sets. Furthermore, we tested the new OOMP2 methodson singlet biradicaloids using Yamaguchi's approximate spin-projection. Unlikethe unregularized OOMP2, which fails to converge these systems due to thesingularity, we show that regularized OOMP2 methods successfully capture strongbiradicaloid characters. While further assessment on larger datasets isdesirable, $\kappa$-OOMP2 with $\kappa$ = 1.45 $E_{h}^{-1}$ appears to combinefavorable recovery of Coulson-Fischer points with good numerical performance.

journal of chemical theory and computation

Regularized Orbital-Optimized Second-Order M{\o}ller-Plesset  Perturbation Theory: A Reliable Fifth-Order Scaling Electron Correlation  Model with Orbital Energy Dependent Regularizers