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As one of the potential candidates of electrocatalysts,non-precious transition metal and nitrogen embedded graphene has attracted extensive attention in recent years.1-6 Deep understanding of the oxygen reduction reaction(ORR)mechanism including specific active sites and reaction pathways would contribute to the further enhancement of their catalytic activity.Our choice of CoNx(x = 2,4)embedded graphene agrees well with the previous experimental evidences that CoNx(x = 2,4)complex in graphene matrix proved to be excellent electrocatalyst for ORR.7-9 We performed density functional theory(DFT)and ab initio molecular dynamics simulations to study the ORR process of CoN4 and CoN2 embedded graphene in acid medium.The calculated formation energy showed that both CoN4 and CoN2 embedded graphene are thermodynamically stable configurations and CoN4 embedded graphene is more stable than CoN2 embedded graphene.The most favorable reaction pathway on CoN4 embedded graphene is the H2O2 formation pathway.However,the CoN4 embedded graphene can not promote a complete 4e-ORR process thus H2O2 is the final product.Meanwhile,the H2O2 dissociation pathway on CoN2 embedded graphene is just right the most favorable pathway,and the energy barrier(0.58 eV)in the rate-determining step is even comparable to Pt electrocatalyst.10-11 In addition,CoN4 complex and CoN2 complex are found to coexist experimentally.All these evidences imply that the CoN2 complex could serve as the second site for the complete ORR process on CoNX embedded graphene catalyst.Therefore,the H2O2 formed on CoN4 complex could be dissociated on CoN2 complex,resulting in a dual-site 2?2e-ORR mechanism,which consists well with the experimental observations.12-13 Finally,the effect of different electrode potentials in the ORR process is also discussed in our work.The free energy diagram revealed that for CoN2,all the ORR steps are downhill at zero potential.Formation of HOOH becomes uphill at U≥0.02 eV,while the formation of the second H2O becomes up hill at U≥0.50 eV.