The activities of 2,3,7,8-tetrachlorinated dibenzo-p-dioxin (2,3,7,8-TCDD), a highly toxic pollutant, and its suitable sorbent from the dioctahedral smectite family are investigated using a range of reactivity indexes using density functional theory (DFT). From the values of the local softness and the charge on the hydrogen atom of the bridging hydroxyl attached to the octahedral metal site present in smectite, used as a first approximation to the local hardness, it is concluded that the local acidities of the inorganic material systems are dependent on several characteristics which are of importance within the framework of the hard and soft acids and bases principle. We first rationalized an understanding of the electronic structure of 7,3,7,8-TCDD, followed by the local softness calculation, to locate its active site. We compared its activity with that of the OH group of the isomorphously substituted (Fe3+, Mg2+, Fe2+, and Li+) dioctahedral smectite family. The recently proposed local hard-soft acid-base principle characterizes the reactive centers of two systems on the basis of equal local softness. We validate the proposition by considering the interaction between systems with different global softnesses, which further paves the way for proposing a novel qualitative way to choose the best sorption material. The results were compared with the interaction energy calculations using DFT. The ordering for best sorption follows the order Mg2+ > Fe2+ > Fe3+ > Li+.