The title reactions over Fe-III and Fe-II-ZSM-5 zeolites are divided into seven and six steps, wherein the M06L:B3LYP energy barriers of N2O decomposition to form active site, benzene activation to form C-O bond and proton transfer to form phenol are equal to 37.0, 13.7, 17.2 and 33.7, 3.0, 19.1 kcal mol(-1), respectively. The active site of Fe-III-ZSM-5 zeolite is geometrically distinct from smaller cluster models and requires conformational transitions before further reactions. The effects of basis sets on reaction energies are carefully investigated, confirming the reliability of default basis sets. The energy differences of MP2:B3LYP with M06L:B3LYP are mainly caused by those steps where adsorbents move significantly within zeolites. Adsorption of benzene is unfavorable in Fe-ZSM-5 zeolite, especially for the divalent state. This is caused by larger repulsive interactions with zeolite framework and will be greatly reduced when forming C-O bond. Adsorbents have nearly no migrations for proton-transfer steps to form phenol, wherein the energy barriers are consistent at these two levels.