The range of U values considered is from 0 eV to 15 eV, with stepwise increments of 0.1 eV. Our study focuses on the adsorption energy of N2, O2, and CO2. This enables us to compare the impact of U on the redox-dependent adsorption of N2, the additional spin effect of O2, and physisorption characteristics of CO2. In particular, for CO2, we study only the end-on Obased adsorption of CO2 and do not consider binding between the metal center and C that is common in chemisorption, following the geometry determined by DFT in ref. .