In summary, the additional orbital relaxations afforded by unrestricted Kohn-Sham (UKS) orbitals in UMRSF result in lower total system energies compared to their restricted open-shell counterparts. This provides extra electron correlation to the MRSF theories, thereby expanding the applicability of MRSF theory to more challenging multi-configurational systems. This improvement enhances the robustness and accuracy of MRSF, making it a versatile tool for studying a wide range of complex electronic structures.