The very wide applications of LTA zeolites, e.g. tritiated water storage, imply that a precise atomic-scale description of the adsorption processes taking place in their structure is crucial. The zeolite structure seems to have a catalytic effect on the O-2/H-2 recombination during the storage process after water radiolysis. To look closely at the conditions that could bring O-2 and H-2 to this particular point, we have conducted investigations using static DFT and systematic ab initio molecular dynamics calculations. We have investigated the interaction of these two molecules with the sodium cations, on which the adsorption capacity of the Na-LTA zeolite depends. The O-2 and H-2 molecules' behaviour inside the cavities is linked to the Na+ position and availability. The latter is regulated by the presence of H2O which interacts with Na+ in a stronger way than O-2 and H-2. Thus, the adsorption studies of different mixtures (O-2/H2O, H-2/H2O and H-2/O-2) have been carried out to characterise the competition between water and other guest molecules. The absence of an obvious interaction between the adsorbates strongly suggests a potential reaction path involving the catalytic effect of the zeolite. Since we have been able to show that the behaviour of O-2 and H-2 molecules is directly affected by the water coverage rate, the reaction path is very likely to be affected too. These results mark a step towards the description of a recombination mechanism between O-2 and H-2 in a zeolite structure, a crucial issue for such systems involving tritiated water adsorbed in nanoporous materials.