We report a B3LYP density-functional theory (DFT) analysis of O-2 adsorption on 27 AunMm (m, n = 0-3 and m + n = 2 or 3; M = Cu, Ag, Pd, Pt, and Na) clusters. The LANL2DZ pseudopotential and corresponding double-zeta basis set was used for heavy atoms, while a 6-311+G(3df) basis set was used for Na and O. We employed basis-set superposition error (BSSE) corrections in the electronic adsorption energies at 0 K (Delta E-ads) and also calculated adsorption thermodynamics at standard conditions (298.15 K and 1 atm), i.e., internal energy of adsorption (Delta U-ads) and Gibbs free energy of adsorption (Delta Gads). Natural Bond Orbital (NBO) analysis showed that all the clusters donated electron density to adsorbed O-2 and we successfully predicted intuitive linear correlations between the NBO charge on adsorbed O-2, O-O bond length, and O-O stretching frequency. Although there was no clear trend in the O-2 binding energy (BE = -Delta E-ads) on pure and alloy dimers, we found the following interesting trend for trimers: BE (MAu2) < BE (M-3) < BE (M2Au). The alloy trimers containing only one Au atom are most reactive toward O-2 while those with two Au atoms are least reactive. These trends are discussed in the context of the ensemble effect and coulomb interactions. We found an approximate linear correlation between the O-2 BE and charge transfer to O-2 for all 27 clusters. The clusters having strongly electropositive Na atoms (e.g., Na-3 and Na2Au) donated almost one full electron to adsorbed O-2, and the BE is maximum on these clusters. Although O-2 dissociation is likely in such cases, we have restricted this study to trends in the adsorption of molecular O-2 only. We also found an approximate linear correlation between the charge transfer and BE versus energy difference between the bare-cluster HOMO and O-2 LUMOs, which we speculate to be a fundamental descriptor of the reactivity of small clusters toward O-2. Part of the scatter in these correlations is attributed to the differences in the O-2 binding orientations on different clusters ( geometric effect). Relatively higher bare-cluster HOMO energy eases the charge transfer to adsorbed O-2 and enhances the reactivity toward O-2. The Frontier Orbital Picture ( FOP) is not always useful in predicting the most favorable O-2 binding site on clusters. It successfully predicted the cluster-O-2 ground-state configurations for 10 clusters, but failed for the others. Finally, the energetics of fragmentation suggest that the bare and O-2-covered clusters reported here are stable.