A theoretical model, based on the vibronic theory of catalysis, has been developed for the CO oxidation reaction catalyzed by gold nanoparticles. The charge fraction transferred between the catalyst and the adsorbed CO molecule depends upon the relative positions of the size-dependent Fermi level of the cluster and the energy levels of the molecular orbitals of CO adsorbed onto the cluster. The charge transferred from the nanocluster to the adsorbed CO molecule increases the absolute values of forces deforming the molecule chemical bond and force constants defining the curvature of potential for nuclear oscillation leading to the decrease in activation energy for CO oxidation. The application of vibronic and jellium theories to CO oxidation provides an explanation of the observed cluster size effects. The relative locations of electronic energy levels of a gold cluster and a CO molecule before and after the adsorption onto the cluster surface. [GRAPHICS] .