Orbital Optimization with Spin-unrestricted and Projected Geminals Reference

Variational improvement of the wave-function at the sacrifice of spin-symmetry is exploited within the antisymmetrized product of strongly orthogonal geminals (APSG) Ansatz. The role of orbital optimization is explored for the unrestricted APSG wave-function, with applying half-projection for partial spin purification, prior to variation. Dynamical correlation is incorporated by a symmetry-adapted formulation of perturbation theory, which corrects for spin along with the effect of perturbation. Splitting between the lowest singlet and triplet levels of cyclobutadiene is investigated along the automerization coordinate of the ground state.