ABSTRACT UiO-66 Metal-Organic framework (MOF) has been highlighted since its synthesis for its stability and many potential applications. Lead (II) and mercury (II) water remediation are among them. In the present work, we used density functional theory calculations, cluster models, and density analysis tools to study the lead and mercury adsorption mechanism of modified UiO-66. We have included the SH (thiol), NCS (isothiocyanate), NMeTU (N-methylthiourea) and DMTD (2,5-dimercapto-1,3,4-thiadiazole) linker groups. The results show a clear trend in capturing both metals: DMTD > NMeTU > SH > NCS. For mercury adsorption, little energy difference for DMTD (bidentate) and NMeTU (monodentate) is found, while for lead, this gap is greater. Inspection of charges and descriptors as softness in conceptual DFT showed the relevance of charge transfer in mercury capture by NMeTU, making this interaction almost as strong as the bidentate fashion through sulfur and nitrogen atoms in DMTD. Lead capture shows charge transfers of lesser magnitude, so the preferred interaction fashion is bidentate. Electronic density difference maps show qualitative visualization of results and are consistent with interaction energies. Through non-covalent interaction (NCI) analysis, it was possible to conclude that at DMTD, the interaction for both metals was stronger with nitrogen atom than sulfur.