The Cluster models of the copper hydroxide structure were constructed to investigate the oxidation of organic substrates containing unsaturated C-C bonds in the Cu(OH)(2)/H2O2 catalytic system. The B3LYP density functional calculations of the activation barriers for ethylene epoxidation by the mono- and binuclear Cut, hydroperoxo complexes corroborated the possibility of non-radical oxygen transfer from the terminal CuOOH hydroperoxo group. The activation barriers presented are relatively high compared to the barriers in the range of 12-15 kcal/mol calculated at the same computational level for Ti-IV hydroperoxo intermediates and Re-VII bisperoxo complexes.