The adsorption, dissociation, and desorption of O-2 on Cu(111), Cu(110), and Cu(100) surfaces at different coverages were studied at the molecular level. The dissociation energies of O-2 molecules increase with the increase in coverage of adsorbed O-2. The saturated coverage of 0 atoms from dissociation of O-2 molecules on Cu(111), Cu(110), and Cu(100) surfaces are 0.25, 0.75, and 0.375 ML, respectively. Based on the computed Gibbs free energies, the relationships between 0 atoms/O-2 molecules and temperature, as well as O-2 partial pressure, on these surfaces are established. Cu(111), Cu( 110), and Cu(100) surfaces are covered by 0 atoms under ultra-high vacuum at 298 K, with 0 atom coverage of 0.25, 0.625, and 0.375 ML, respectively. Phase diagrams provide useful information on phase transition from Cu to Cu20 in terms of temperature and O-2 partial pressure. Results of this study may provide guidance in investigating the interaction between O-2 and transition metals. (C) 2016 Published by Elsevier B.V.