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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 (ScNxC3−x@SACs and ScNxC4−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 ScNxC3−x@SACs and ScNxC4−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-NxC3−x@SACs and Sc-NxC4−x@SACs provides a method for studying the catalytic performance of other rare earth elements.