We have studied effect of alkali and alkaline earth metal cations (Liþ, Naþ, Kþ, Be2þ, Mg2þ) decoration on hydrogen adsorption of the organic linker of Zn2(NDC)2(diPyTz) by employing three cluster models: diPyTz:mLiþ (m ¼ 1e4), diPyTz:mLiþ:nH2 (m ¼ 0,1,2 and n ¼ 1e5) and diPyTz:1Mþ:1H2 (Mþ ¼ Naþ, Kþ, Be2þ, Mg2þ) complexes, using density functional theory (DFT) and second-order MollerePlesset perturbation theory (MP2). The calculated binding energies show that decoration of the organic linker with alkali and alkaline earth metal cations enhanced H2 interaction with diPyTz when compared with the pristine diPyTz. The atomic charges were derived by Mulliken, ChelpG and ESP methods. Finally, the atoms in molecules theory (AIM) were also applied to get more insight into the nature of the interaction of diPyTz and Liþ. Results of AIM analysis show that NeLiþ bond in diPyTz organic linker's complex appears as shared electron interaction.