The isomerization reactions of HOOX -> HOXO -> HXO2 (X = Cl, Br, I) have been studied by using the density functional theory. The breakage and formation of the chemical bonds of the titled reactions have been discussed by the topological analysis method of electronic density. The calculated results show that there is a transitional structure of a three-membered ring on each of the isomerization reaction paths. The "energy transition state (ETS)" and the "structure transition state (STS)" in all of the studied reactions have been found. In all these reactions, the position of the structure transition state and the scope of the structure transition region correlate well with the reaction energy. The STS appears after the ETS in the exothermic reaction but it appears before the ETS in the endothermic reaction. The less reaction energy there is, the wider scope of the structure transition region.