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Quantum chemical simulation of catalytic processes involving the thiolated Au NCs has great prospect and provides new thermodynamic and kinetic data, as well as theoretical information concerning the ligand effect and the mechanism of reaction at atomic level. Here we present the results of calculation of Au20(SR)16(R=CH3, Ph) in gas phase, solution and supported on CeOx. Different types of cluster’s activation at heating were considered. The O2 and CO adsorption on the cluster, and CO oxidation was simulated. Spin–polarized DFT/PBE level in the scalar–relativistic approach was used.