The interaction energies (IEs) of H₂ and various organic ligands have been computed using coupled-cluster method with singles, doubles, and noniterative triples (CCSD(T)) at the complete basis set (CBS) limit. The density fitting-density functional theory-symmetry adapted perturbation theory (DF-DFT-SAPT) approach has been used to probe the nature of interaction between H₂ and organic linkers. It has been found that dispersive interaction predominantly stabilizes the intermolecular complex formation of H₂ on a variety of organic linkers. Furthermore, H₂ binding affinity of inorganic connectors is improved by partial isomorphic substitution of Zn by different metal ions such as Fe, Co, Ni and Cu. A new modified metal-organic framework (MOF-5 M) has been designed based upon the insight from the organic and inorganic fragments. The present study provides valuable information required for the design of novel MOFs with improved affinity for H₂ adsorption.