Two single-reference approaches to singlet biradicaloid problems: Complex, restricted orbitals and approximate spin-projection combined with regularized orbital-optimized Moller-Plesset perturbation theory

We present a comprehensive study of two single-reference approaches to singlet biradicaloids. These two approaches are based on the recently developed regularized orbital-optimized Moller-Plesset method (kappa-OOMP2). The first approach is to combine Yamaguchi's approximate projection (AP) scheme and kappa-OOMP2 with unrestricted (U) orbitals (kappa-UOOMP2). By capturing only essential symmetry breaking, kappa-UOOMP2 can serve as a suitable basis for AP. The second approach is kappa-OOMP2 with complex, restricted (cR) orbitals (kappa-cROOMP2). Although its applicability is more limited due to the comparative rarity of cR solutions, kappa-cROOMP2 offers a simple framework for describing singlet biradicaloids with complex polarization while removing artificial spatial symmetry breaking. We compare the scope of these two methods with numerical studies. We show that AP+kappa-UOOMP2 and kappa-cROOMP2 can perform similarly well in the TS12 set, a dataset that includes 12 data points for triplet-singlet gaps of several atoms and diatomic molecules with a triplet ground state. This was also found to be true for the barrier height of a reaction involving attack on a cysteine ion by a singlet oxygen molecule. However, we also demonstrate that in highly symmetric systems like C-30 (D-5h), kappa-cROOMP2 is more suitable as it conserves spatial symmetry. Finally, we present an organic biradicaloid that does not have a kappa-cROOMP2 solution in which case only AP+kappa-UOOMP2 is applicable. We recommend kappa-cROOMP2 whenever complex polarization is essential and AP+kappa-UOOMP2 for biradicaloids without essential complex polarization but with essential spin-polarization. Published under license by AIP Publishing.