9 FH1 and FH2 states to dissociate are both found to be 0.25 eV, which are larger than the smallest energy barrier from the HH1 state of 0.22 eV. The electronic properties are then analyzed for the dissociation path shown in Fig. 7(a), whose energy barrier is the smallest during the dissociation from molecular adsorption pre- cursor states. The PDOS around the two oxygen atoms are calculated for the corresponding initial, transition and final states. As shown in Fig. 8(a), the π ⋆ p antibonding orbital of O$_{2}$ are broadened and shifted below the Fermi energy in the HH1 adsorption state, through hybridizations with p electronic states of Pb. At the transition state of the dissociation process, the energy interval between the σ$_{s}$ and σ ⋆ s orbitals is decreased from 6.58 to 6.24 eV, and the oxygen 2 p states hybridize in a different way with electronic states of Pb from that in the HH1 adsorption state. At the end of the dissociation process, the two oxygen atoms relax into two neighboring hollow sites, and the molecular orbitals of O$_{2}$ all disappear after electronic hybridizations. After the systematic studies on the O$_{2}$ dissociation in different ways, we reveal that the most energetically favorable one is from the HH1 adsorption state into two neighboring hollow sites. It is always believed that because of the confinement of the two boundaries in the vertical direction, the quantum behavior of electrons will cause a number of unique properties for thin metal films that could be superior to their bulk counterpart. In particular, quantum size effects on surface reactivity have been studied extensively for applications in catalysis, corrosion, and gas sensing. Here we further consider the dissociation path for O$_{2}$ molecules on different Pb(111) films, including both the dissociation along the T- and B- x, y channels from O$_{2}$ gases, and the dissociation from molecular adsorption states. After systematic calculations, we find that the most energetically favorable dissociation paths are the same on different Pb(111) films, i.e. from the HH1 adsorption state to the atomic adsorption of two oxygen atoms at two neighboring hollow sites. Figure 9 shows the 2D PES cuts for the O$_{2}$ dissociation on 4 ∼ 7 monolayers Pb(111) films. The calculated energy barriers are respectively 0.26, 0.22, 0.26 and 0.24 eV. Since many properties of Pb(111) films such as work function and surface energy show bilayer oscillation behaviors because of QSE $^{25}$. The even-odd oscillation of the dissociation energy barrier proves the modulation of QSE on the O$_{2}$ dissociation on Pb(111) films.