Theoretical insights for CoN_xC_4-x-graphene (x = 0–4) materials as high performance low-cost electrocatalysts for oxygen reduction reactions

Transition metal-doped two-dimension carbon matrices have attracted particular interest as oxygen reduction reaction (ORR) catalysts because of their low-cost, good conductivity of electricity, and promising applications in fuel cells and metal-air batteries. Herein, a density functional theory study is performed on the CoN_xC_4-x (x = 0–4) embedded graphene to investigate the effect of N atoms doping number and doping configurations. The calculated formation energy and average bond length of Co–C/N drop off with the increase in N atoms of the CoN_xC_4-x graphene system. The most stable adsorption configurations and the relevant adsorption free energies of key ORR intermediates on Co–N sites toward the CoN_xC_4-x graphene system are obtained, indicating that N doping levels and doping configurations have a regular influence on this system. On this basis, scaling relations can be obtained among the adsorption free energies of *OH, *OOH, and *O. The volcano plot of ORR theoretical overpotential $(ηth)$ using $ΔG*OH−ΔG*O$ as a descriptor was further established, which revealed that $ηth$ is influenced by the adsorption mode and the free energy change in the active site. For all studied systems, the ORR substeps are all downhill at zero potential from the plotted free energy diagrams. The density of states is employed to further illustrate that the hybridization between the Co atom and the O atom is a deterring factor on electrocatalyst activity. These calculations reveal the influence of nitrogen atom doping in Co–N-graphene catalysts and afterward point a direction for designing high-performance non-precious metal ORR electrocatalysts.