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We present a comprehensive study of two single-reference approaches tosinglet biradicaloids. These two approaches are based on the recently developedregularized orbital-optimized M{\o}ller-Plesset method ($\kappa$-OOMP2). Thefirst approach is to combine the Yamaguchi's approximate projection (AP) schemeand $\kappa$-OOMP2 with unrestricted (U) orbitals ($\kappa$-UOOMP2). Bycapturing only essential symmetry breaking, $\kappa$-UOOMP2 can serve as asuitable basis for AP. The second approach is $\kappa$-OOMP2 with complex,restricted (cR) orbitals ($\kappa$-cROOMP2). Though its applicability is morelimited due to the comparative rarity of cR solutions, $\kappa$-cROOMP2 offersa simple framework for describing singlet biradicaloids with complexpolarization while removing artificial spatial symmetry breaking. We comparethe scope of these two methods with numerical studies. We show thatAP+$\kappa$-UOOMP2 and $\kappa$-cROOMP2 can perform similarly well in the TS12set, a data set that includes 12 data points for triplet-singlet gaps ofseveral atoms and diatomic molecules with a triplet ground state. This was alsofound to be true for the barrier height of a reaction involving attack on acysteine ion by a singlet oxygen molecule. However, we also demonstrate that inhighly symmetric systems like $\text{C}_{30}$ ($\text{D}_{5h}$)$\kappa$-cROOMP2 is more suitable as it conserves spatial symmetry. Lastly, wepresent an organic biradicaloid that does not have a $\kappa$-cROOMP2 solutionin which case only AP+$\kappa$-UOOMP2 is applicable. We recommend$\kappa$-cROOMP2 whenever complex polarization is essential andAP+$\kappa$-UOOMP2 for biradicaloids without essential complex polarization butwith essential spin-polarization.

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Two Single-Reference Approaches to Singlet Biradicaloid Problems:  Complex, Restricted Orbitals and Approximate Spin-Projection Combined With  Regularized Orbital-Optimized M{\o}ller-Plesset Perturbation Theory