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 ${(\eta }_{th})$ using ${\Delta G}_{*OH}{-\Delta G}_{*O}$ as a descriptor was further established, which revealed that ${\eta }_{th}$ 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.

中文翻译：

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CoNxC4-x-石墨烯（x=0-4）材料作为用于氧还原反应的高性能低成本电催化剂的理论见解

过渡金属掺杂的二维碳基质作为氧还原反应 (ORR) 催化剂引起了特别的兴趣，因为它们成本低、导电性好，并且在燃料电池和金属空气电池中的应用前景广阔。在此，对 CoN _x C _4-x (x = 0–4) 嵌入的石墨烯进行了密度泛函理论研究，以研究 N 原子掺杂数和掺杂配置的影响。Co-C/N 的计算形成能和平均键长随着 CoN _x C _4-x石墨烯系统中 N 原子的增加而下降。最稳定的吸附构型和关键 ORR 中间体在 Co-N 位点上对 CoN _x C的相关吸附自由能_{获得了 4-x}石墨烯系统，表明 N 掺杂水平和掺杂配置对该系统有规律的影响。在此基础上，可以得到*OH、*OOH和*O的吸附自由能之间的标度关系。ORR理论过电位的火山图${(\eta }_{吨H})$ 使用 ${\Delta G}_{*哦H}{-\Delta G}_{*哦}$ 作为进一步建立的描述符，这表明 ${\eta }_{吨H}$受吸附模式和活性位点自由能变化的影响。对于所有研究的系统，从绘制的自由能图中，ORR 子步骤都在零电位处下坡。态密度用于进一步说明 Co 原子和 O 原子之间的杂化是电催化剂活性的阻碍因素。这些计算揭示了氮原子掺杂对 Co-N-石墨烯催化剂的影响，并为设计高性能非贵金属 ORR 电催化剂指明了方向。