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The coordinatively unsaturated chromium(II)‐based Cr3[(Cr4Cl)3(BTT)8]2 (Cr−BTT; BTT3−=1,3,5‐benzenetristetrazolate) metal–organic framework (MOF) has been shown to exhibit exceptional selectivity towards adsorption of O2 over N2/H2. Using periodic density functional theory (DFT) calculations, we attempted to decipher the origin of this puzzling selectivity. By computing and analyzing the magnetic exchange coupling, binding energies, the partial density of states (pDOS), and adsorption isotherms for the pristine and gas‐bound MOFs [(Cr4(X)4Cl)3(BTT)8]3− (X=O2, N2, and H2), we unequivocally established the role of spin states and spin coupling in controlling the gas selectivity. The computed geometries and gas adsorption isotherms are consistent with the earlier experiments. The binding of O2 to the MOF follows an electron‐transfer mechanism resulting in a CrIII superoxo species (O2.−) with a very strong antiferromagnetic coupling between the two centers, whereas N2/H2 are found to weakly interact with the metal center and hence only slightly perturb the associated coupling constants. Although the gas‐bound and unbound MOFs have an S=0 ground state (GS), the nature of spin the configurations and the associated magnetic exchanges are dramatically different. The binding energy and the number of oxygen molecules that can favorably bind to the Cr center were found to vary with respect to the spin state, with a significant energy margin (47.6 kJ mol−1). This study offers a hitherto unknown strategy of using spin state/spin couplings to control gas adsorption selectivity in MOFs. [ABSTRACT FROM AUTHOR]