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The development of a stable catalyst with excellent catalytic performance for the oxygen evolution reaction (OER) in alkaline environments is a key reaction in various electrochemical technologies. In this work, single-atom catalysts (SACs) systems in which scandium (Sc), a rare earth metal, with different N/C coordination environments (ScN_xC_3−x@SACs and ScN_xC_4−x@SACs of Sc) were systematically studied with the help of density functional theory (DFT) calculations. The results of the structural thermodynamic stability analysis indicated that the ScN_xC_3−x@SACs and ScN_xC_4−x@SACs systems are more stable with increasing N atom doping concentration around Sc. The ScN₃, ScN₃C, and ScN₄ with better stability were selected as the objects of subsequent research. However, ScN₃ and ScN₄ form Sc(OH)₂N₃ and Sc(OH)₂N₄ structures with double-hydroxyl groups as ligands because of the strong adsorption of OH species, whereas the strong adsorption of OH species by ScN₃C causes structural instability. Here, the overpotential (η) of Sc(OH)₂N₃ was 1.03 V; Sc(OH)₂N₄ had two reaction paths and the η of path 1 was 0.80 V, which was 0.30 V lower than that of path 2. Therefore, Sc(OH)₂N₄ can be used as a stable and promising OER catalyst with easy desorption of O₂ and good cycle performance. The hydroxyl ligand modification of Sc-N_xC_3−x@SACs and Sc-N_xC_4−x@SACs provides a method for studying the catalytic performance of other rare earth elements.