We investigated the dioxygenation of nitrile activation by $[Co(III)(TBDAP)(O_2)]^+$ (TBDAP = N,N-di-tert-butyl-2,11-diaza[3,3](2,6)-pyridinophane) using density functional theory. The proposed mechanism based on the experiments, which is an intermolecular cycloaddition, is proved not to operate through our calculations. Instead, new mechanism that the terminal superoxo formed by the nitrile coordination reacts with the nitrile-carbon is more likely. The cobalt complex can have various spin states because the TBDAP ligand changes the d orbital energy levels and the reaction traverse through the spin state which shows the lowest energy.