Perturbative corrections to the equation-of-motion spin–flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals

We present perturbative corrections to a recently introduced spin–flip self-consistent field (SF-SCF) wave function. The spin–flip model describes both closed and open shell singlet states within a single reference formalism as spin–flipping, e.g., $\mathrm{\alpha \to \beta ,}$ excitations from a triplet ${\mathrm{(M}}_s\text{=1)}$ reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding singlet state. The simplest spin–flip model employs a SCF wave function for the reference state, and the resulting equations for target states are therefore identical to configuration interaction singles (in spin–orbital form). While being a qualitatively correct zero-order wave function, SF-SCF should be augmented by dynamical correlation corrections to achieve a quantitative accuracy. The results demonstrate that the second-order approximation to the more theoretically complete spin–flip coupled-cluster model (truncated at double substitutions) represents a systematic improvement over the SF-SCF model.