The catalytic oxidation of molecular oxygen based on nitroxide radical organocatalysts is one of the hot topics in the field of catalysis in recent years. The structures and catalytic activity of the nitrogenous six membered heterocyclic ring obtained by the pyridine ring and the pyrazine ring substituted for the benzene ring of N-Hydroxyphthalimide (NHPI) were studied by theoretical methods. The effect of protonic acid HCl on the catalytic activity of this kind of catalyst was investigated. The results show that the catalytic activity of nitrogenous six membered heterocyclic ring catalyst is higher than that of NHPI, even some of the catalyst is comparable to that of N,N′dihydroxypyromellitimide (NDHPI); pyrazine pyridine ring chain is helpful to improve the catalytic activity of the catalyst; HCl hydrogen bond interaction with the aromatic ring of these catalysts can improve the catalytic activity of the catalyst. This study is helpful to deepen the understanding of the intrinsic activity of this kind of catalyst and also to provide theoretical guidance for the catalytic mechanism and catalytic oxidation experiment of this kind of catalyst.