We present a molecular simulation study on the most suitable zeolite topologies for hydrogen adsorption and storage. We combine saturation capacities, pore size distributions, preferential adsorption sites, and curves of heat of adsorption of hydrogen as a function of temperature (we call them heats of adsorption (HoA)-curve) to identify the optimal zeolites for storage and release of hydrogen. Then, we analyze the relation between the shape of the HoA-curve and the topology of the materials. We also evaluate the influence of incorporating Feynman-Hibbs effect on the adsorption behavior. We can establish different shapes on the HoA-curve depending on the uniformity or not of the pores of the zeolites. Parabola-like curves are observed in structures with one or similarly sized pores, whereas deviations from the parabola are found at low temperature for structures combining large and small pores. The Feynman-Hibbs quantum correction reduces the adsorption capacity of the materials affecting not only the saturation capacity but also the shape of the isotherms. From our results, the zeolites studied in this work can be considered potential candidates for the storage and release of hydrogen.