After obtaining fully relaxed UKS MOs from variational SCF, the MO reordering scheme is applied before the response part of the computation. Since MO reordering can potentially alter the corresponding response energies, our scheme prevents the MO exchange between occupied and virtual spaces, which changes the phase of the reference state without affecting the reference energy of UKS. Furthermore, we obtained the approximate ⟨S 2 ⟩ values of UMRSF using the auxiliary wave function and measured the degree of spin contamination in UMRSF.