Hydrogen adsorption efficiency of different Cu(I)-AH systems (AH = Imidazole, Isoxazole, Isothiazole, Pyrazole, Thiazoleand Oxazole) have been studied. The Cu(I)-AH systems are stabilized in cationic state, adsorb H2 in molecular form and found to be a promising hydrogen storage system as per Department of Energy (DOE), USA, standard. The bonding nature in between Cu(I)-AH and Cu(I)-AH---H2 has been investigated by ELF (electron localization function) study and NCI (non-covalent interaction) analysis, and found to be non-covalent in nature. All the systems can adsorb up to five molecular H2 in a quasi-adsorption process. All the systems show the negative Gibbs free energy change at 117K.