We have performed a computational modelling of proton exchange reaction activated by the Brønsted acid sites of H-ZSM-5 and H-MCM-22 zeolites involving CH 4 molecule. We have taken advantage of the effectiveness of the in-house developed CPMD/GULP interface program and TASS enhance sampling approach to study this reaction at 300 K. Through extensive simulations, we computed the free energy barrier of the proton exchange reaction as 29.2 ± 0.9 kcal mol -1 and 31.3 ± 1.0 kcal mol -1 for H-ZSM-5 and H-MCM-22 zeolites, respectively. The trend in the free barriers is in agreement with the previous reports.