Density Functional Theory (DFT) calculations were used to investigate the interaction of hydrogen and deuterium in different orientations with different adsorption sites in finite-size cluster models of Cu2(bmc)4 and Zn2(bmc)4 paddle wheels that cut out from two important metal organic frameworks (MOFs), Cu-BTC and Zn-BTC. DFT calculations in the context of Orca program package with B3LYP exchange correlation functional accompanied with def2-tzvp and LANL basis sets were used to get single point energy for each of the basis sets. Binding energies of a single and double H2/D2 molecule adsorbed on Cu2(bmc)4 and Zn2(bmc)4 paddle wheel units in several orientations with optimized Cu–H and Zn–H distances were reported. The results compare well with the results of Infrared spectra measurements on Cu2(bmc)4 structure. Additionally, thermal desorption spectroscopy (TDS) measurements revealed three different adsorption sites for H2 and D2 on Cu2(bmc)4 structure. The adsorption/desorption potential of hydrogen isotopes and selectivity of Cu-BTC MOF with different available adsorption sites was exploited by performing TDS measurements.