The kinetic and thermodynamic characteristics of oxygen penetration of palladium (111) surface are studied using the DFT cluster method. The activation energy and the energy difference between the adsorbed and subsurface states of oxygen atom as well as the corresponding frequency and geometrical characteristics are computed from the minimum energy paths describing the penetration process. A simple analytical model of this process is suggested and is applied in order to gain insight into its mechanism and estimate its rate. This approach is used to predict the trends in the activation barriers for the penetration of a single oxygen atom on several transition metals showing Pd to have the lowest barrier (37 kcal/mol as opposed to 44-46 kcal/mol with Pt, Ru, Rh, and Ir). It is also applied to show that the dependence of the activation energy on the reaction heat is described by the linear BEP relation and that the activation barrier declines with the oxygen coverage of (111) palladium surface.