Oxygen atom transfer reaction between ML3=0 and ML3 (L=2,4,6-trdmethylphenyl (Mes) for M=Ir and L=2,6-diisopropylphenylimide (NAr) for M=Os) was theoretically investigated by DFT method. The optimized geometry of (Mes)(3)Ir-O-Ir(Mes)(3) agrees well with the experimental one, although those of (CH3)(3)Ir-O-Ir(CH3)(3) and Ph3Ir-O-IrPh3 are much different from the experimental one of the Mes complex. These results indicate that the bulky ligand plays important roles to determine geometry of the mu-oxo Binuclear Ir complex. Theoretical study of the real systems presents clear pictures of these oxygen atom transfer reactions, as follows: In the Ir reaction system, (i) the mu-oxo bridged Binuclear complex is more stable than the infinite separation system in potential energy surface, indicating this is incomplete oxygen atom transfer reaction which does not occur at very low temperature, (ii) unsymmetrical transition state is newly found, in which one Ir-O distance is longer than the other one, (iii) unsymmetrical local minimum is also newly found between the transition state and the infinite separation system, and (iv) activation barrier (Ea) is very small. In the Os reaction system, (v) the transition state is symmetrical, while no intermediate is observed unlike the Ir reaction system, and (vi) Ea is very large. These results are consistent with the experimental results that the reaction rapidly occurs in the Ir system but very slowly in the Os system, and that the mu-oxo bridged dinuclear intermediate is detected in the Ir system but not in the Os system. To elucidate the reasons of these differences between Ir and Os systems, the Ea value is decomposed into the nuclear and electronic factors. The former is the energy necessary to distort ML3 and ML3=O moieties from their equilibrium geometries to those in the transition state. The latter depends on donor-acceptor interaction between ML3=O and ML3. The nuclear factor is much larger in the Os system than in the Ir system and it contributes to about 70% of the difference in Ea. The energy gap between the donor orbital of ML3 and the acceptor orbital of ML3=O is much larger in the Os system than in the Ir system, which also contributes to the lower Ea value of the Ir system than that of the Os system.