The structure-reactivity relationship of new hydroxyimide organocatalysts based on the heterocyclic replacements of the phenyl ring of N-hydroxyphthalimide (NHPI) has been theoretically investigated to gain a mature understanding of this particular catalysis for aerobic oxidation. We find that the reactivity of catalysts with the common five-member aromatic rings is lower than that of NHPI. The catalyst with the recyclable structure of imidazolium ionic liquid may serve as a novel model catalyst for further improvements due to its reactivity comparable to that of NHPI. The catalytic reactivity of multi-nitroxyl catalysts is theoretically more fascinating than that of the highly efficient N,N-dihydroxypyromellitimide. (C) 2016 Elsevier B. V. All rights reserved.