▎ 摘　　要

The lack of efficient catalysts and research on the mechanism for the methanol oxidation reaction (MOR) impedes the development of direct methanol fuel cells. In this work, based on density functional theory calculations, we systematically investigated the activity trends of electrochemical MOR on a single transition-metal atom embedded in N -coordinated graphene (M@N4C). By calculating the free energy diagrams of MOR on M@ N4C, Co@N4C was screened out to be the most effective MOR catalyst with a low limiting potential of 0.41 V due to the unique charge transfers and electronic structures. Importantly, one-and two-dimensional volcano relationships in MOR on M@N4C catalysts are established based on the d-band center and the Gibbs free energy of Delta G(*CH3OH) and Delta(G*CO), respectively. In one word, this work provides theoretical guides toward the improved activity of MOR on M@N4C and hints for the design of active and efficient MOR electrocatalysts.