In spin-flip formalism, such as SF-TDDFT, spin contamination arises from the absence of specific configurations in the response space. Additionally, spin contamination from orbital asymmetries also occurs in unrestricted formulations. The MRSF formulation addresses this issue by including the missing configurations, thereby eliminating spin contamination from the response space. However, spin contamination due to orbital asymmetries can still persist. Unlike the Kohn-Sham (KS) molecular orbitals (MOs) in DFT, the wavefunction in response theories corresponds to an auxiliary wavefunction, which is the solution to the orbital Hessian matrix. As a result, the approximate expectation value of ⟨S 2 ⟩ can be obtained by applying the operator to the auxiliary wavefunction.