N,N-dihydroxypyromellitimide (NDHPI) and N,N′,N′′-trihydroxyisocyanuric acid (THICA) have been recently demonstrated to act as better carbon-radical-producing catalysts than the popular N-hydroxyphthalimide (NHPI). To gain a mature understanding of these particular catalysts, herein their geometrical, electronic, and thermochemical properties, as well as their catalytic activities, have been systemically investigated by a theoretical analysis. It appears that THICA, unlike NDHPI and NHPI, is unsuitable for solvent-free catalysis or catalysis in aprotic solvents due to its favorable coexistent planar conformer. Besides, the more remarkable catalytic efficiencies of NDHPI and THICA compared to NHPI can be ascribed to the lower barriers and the endothermicity in the H-abstraction processes by their radicals, especially by their multi-radicals which show stronger electron-withdrawing effects. Furthermore, the generation of THICA radicals would be much feasible at high temperature without co-catalysts. This study provides a new perspective towards the rational design of reactive hydroxyimide organocatalysts for industrial applications.