Quantum-chemical calculations give insight in the experimentally observed higher rate of hydrogen-deuterium exchange for oxidized Ga/HZSM-5 over reduced Ga/HZSM-5. The reaction is computed to be more facile over reduced (Ga+) than over oxidized (GaO+) cations. The difference lies in the difficult formation of active GaH2+ cations from Ga+ compared to facile hydrogen dissociation over GaO+ to give active GaHOH+ cations. Neutral gallium oxide clusters are shown to have a lower intrinsic activity than GaO+ cations.