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Single-atom catalysts (SACs) are promising for 4e−oxygen reduction reaction (4e−ORR). However, they are rarely utilized in other oxygen-involved reactions, e.g. 2e−ORR to produce H2O2, 4e−oxygen evolution reaction (4e−OER), and 2e−water oxidation reaction (2e−WOR). Herein, we applied density functional theory (DFT) calculations to investigate the applicabilities of SACs, including Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Nb, Mo, Ru, Rh, Pd, Pt, and Au with axial coordination (e,g, –OH, =O, and ≡N) for all 4e−/2e− oxygen reactions. With axial coordination, SACs derived from early transition metals exhibit high catalytic performance, including V-SAC-OH with an overpotential of 0.61 V for 4e−ORR, Mo-SAC-OH with an overpotential of 0.05 V for 2e−ORR, Mo-SAC-O with an overpotential of 0.52 V for 4e−OER, and Nb-SAC-OH with an overpotential of 0.14 V for 2e−WOR. Among them, most SACs deliver a trend of adsorption-energy decreasing with the increase of axial bond, which successively meets various adsorption requirements of all 4e−/2e− oxygen reactions. This finding has led to the discovery of highly active SACs adapted to different oxygen reactions. Importantly, an intrinsic framework that combines SAC configuration, transition metal (TM) species, and TM charges was established to describe the adsorption ability of SACs. This work offers an intrinsic landscape to understand the correlation of the adsorption ability of SACs with the tendentiousness of oxygen-involved reactions and guides the rational design of SACs.