Radioactive Xe and Kr released from nuclear reactors and spent nuclear fuel reprocessing plants can be converted in to useful ones after the radioactive decay. The adsorption techniques employing porous materials are a cost effective solution for the capture of these volatile radionuclides compared to expensive cryogenic distillation process. Among various porous materials, metal-organic frameworks (MOFs) show excellent storage and separation properties. In this paper, we investigate the Xe and Kr adsorption properties of recently reported SBMOF-2 using van der Waals corrected density functional theory. In particular, SBMOF-2 has two types of pores with distinct linker groups along pore channels. Our studies show that Xe is preferred over Kr in both the pore channels, which are in complete agreement with experimental observations. The adsorption energies obtained for SBMOF-2 is comparable to other efficient MOFs reported in the literature for Xe/Kr separation. The two pore channels show slightly different binding energies depending on their linker groups and pore characteristics. The impact of central metal atom on adsorption properties is evaluated. A new SBMOF-2(Mg) with magnesium as central metal atom shows Xe/Kr adsorption behavior similar to the experimentally studied SBMOF-2(Ca). Next, we have investigated the effect of polarizable groups in the pore channels where linker hydrogen atoms are substituted with halogen atoms. There is a significant increase in the adsorption energy of noble gases in the halogenated pore channels. Due to the presence of halogen atoms, electron charge density redistribution takes place in the MOF network leading to permanent dipoles. Accordingly, the adsorption energies increase with the polarizability of halogen atoms. The ab initio calculations performed in this study suggest that Xe/Kr separation properties of MOFs depend upon many competing interactions, which originate from their structural and chemical properties.