Fig.5. (a) the LSV curve of CoFe-Co_xN@NC for OER before and after the 80000 s cycle at a constant current density of 10 mA·cm⁻², (b) the chronopotentiometri measurement of recorded at a constant current density of 10 mA·cm⁻²for CoFe-Co_xN@NC

In order to provide insights into the electrocatalytic mechanism of CoFe-Co_xN@NC for OER, DFT calculation was employed to investigate and compare the OER catalytic performances of four catalyst models including naked FeCo alloy, FeCo alloy encapsulated by carbon layer (CoFe@C), CoFe alloy encapsulated by nitrogen-doped carbon layer (CoFe@NC), and the as-prepared CoFe-Co_xN@NC. Generally, OER undergoes a four-electron step pathway in a basic electrolyte showed as Fig. 6a. The Gibbs free energy profiles for four catalysts were depicted in Fig. 6b, and the rate-determining step (RDS) with the value of the Gibbs free energy barrier was highlighted, where a fairly high Gibbs free energy barrier of 1.71 eV was obtained at 1.23 V for OER over naked CoFe alloy. The reason for this mainly attributed to the strong absorption (a Gibbs free energy barrier of -1.93 eV) of the active oxygen on the surface of CoFe alloy to form an excessively stable *O intermediate for OER. The charge density differences presented in Fig. S13 showed that charges were almost transferred onto the surface of oxygen atom, further revealing the enhanced electrostatic interaction between oxygen and CoFe alloy. In such case, more energies were required to overcome the barrier from *O to *OOH, resulting in the high overpotential for OER over CoFe alloy. Theoretically, CoFe alloy encapsulated by graphitic carbon layer can prevent it from the direct contact with reactive oxygen species, however, the interfacial distance between CoFe alloy and graphitic carbon layer would affect the stability and charge transfer. It can be seen from Fig. 6c that the total energy of the CoFe@C heterojunction catalyst was lowest when the interfacial distance reached 4Å. Nevertheless, the electrons mainly accumulated in its interfacial space at its most stable configuration based on the charge density difference showed in Fig. 6c inserted images, making the active site to *OH pathway as the RDS with the high energy barrier of 1.56 eV. Interestingly, doping nitrogen in the graphitic carbon layer can redistribute the charge density without sacrificing its stability. The electrons transferred from CoFe alloy can be well distributed on the nitrogen-doped graphitic carbon layer as described in Fig. 6d-e, promoting the OER process with a lower energy barrier of 0.68 eV at RDS from *O to *OOH. Actually, in this study, in situ nitrogen-doping pyrolysis process can form a specific heterojunction CoFe-Co_xN@NC with three phases, nitrogen-doped Co_5.47N-connected CoFe alloy. The Co_xN as a linker can induce the uniform distribution of charge density as shown in Fig. 6f based on the DFT simulation, which could optimize the adsorption/desorption strength of the OER intermediates and products. As a result, a lowest limiting energy barrier of 0.43 eV can be achieved by DFT calculation at 1.23 V for OER over CoFe-Co_xN@NC (Fig. 6b) in comparison with other used catalysts, in consistent with the trend of experimental results.