The tetrahedral paramagnetic di-cobaltous complex is an important class of coordination compounds that have many applications in various fields such as catalysis, single molecular magnet (SMM), and spintronics[1], using BP86 functional[24] with def2-TZVP[25], basis set, while the broken symmetry theoretical method was conducted by B3LYP functional, the reactivity of the synthesized paramagnetic di cobaltous [Co2LI2OH] + complex[2] can be enhanced by the lowering HOMO-LUMO gap effect of oxo bridging ligand instead hydroxo ligand, also from the different theoretical approaches for calculating the exchange coupling constant to tetrahedral paramagnetic di-cobaltous complex, we found that the best approach was achieved by Noodlman treatment[3], also for such chemical environments the best calculated spin population was generated by Mulliken spin analysis.