Quantum theoretical calculations have been performed to obtain the lowest energy reaction path for the oxidation of an Al micro-cluster with an O-2 molecule. In reactions with a ground state O-2 molecule(spin triplet state), a very low potential energy barrier of 0.2 eV exists for the adhesion of an O-2 molecule to an Al cluster and the stabilization energy of the final product is 3.0 eV. In reactions with an electronically excited O-2 molecule (spin singlet state), no energy barrier exists during the reaction and the oxidation of the Al cluster proceeds spontaneously, giving a stabilization energy of 7.7 eV. Since the ground electronic state of the initial reactant is the triplet state and the most stable final product is the singlet state, an inter-system crossing from the triplet to the singlet state is expected to occur during the oxidation process.