In current decade all countries are going to launch their National Hydrogen Energy Mission with ambitious targets in the renewable energy sector and the push for hydrogen energy will steer the world in promising direction towards green energy. Scientist, technologists, and industrialist are searching for a suitable hydrogen storage system. Influenced by our promising recent findings on Li doped aromatic N-heterocyclic (ANH) six-membered Py-Li systems; (Py = Pyrazine, Pyrimidine, Pyridazine, and Triazine), here we have focused on isomeric oxadiazole-xLi+ (x = 1,2) templates. The hydrogen trapping ability of the systems have been studied carefully with density functional theory (DFT) approach. The aromaticity of the systems prevails even after hydrogen adsorption and the process is qausi-molecular in nature. It justifies these templates as potential hydrogen storage material. The charge on the Li atom decreases gradually with each successive H2 adsorption, and a charge transfer type interaction occurs from the bonding orbital (BD) of H2 molecules to the antibonding lone pair orbital (LP*) of Li+ ion. It is found that, the molecular H2 interacts with oxadiazole-xLi+ template through ionic type bonding. Gibbs free energy changes suggest that the H2 adsorption process is spontaneous at or below 200 K.