V. CONCLUSION Acknowledgments In summary, we have investigated the adsorption and dissociation of O$_{2}$ molecules on different Pb(111) films. The electronic states of an O$_{2}$ molecule in close to the Pb films are firstly analyzed and imply that the adiabatic calculations are reliable. For the molecular adsorption precursor states, we find that the electronic interactions are very similar in the HH1 and HH2 states, and they are thus two nearly degenerate states. Besides, we further point out that no s - p hybridizations in Pb(111) films is the main reason for the existence of molecular adsorption precursor states. Based on our adiabatic PES calculations, we find that the dissociation of O$_{2}$ from the molecular adsorption precursor states have lower energy barriers than from O$_{2}$ gases. The most energetically favorable dissociation paths on different Pb(111) films are found to be the same, which is from the HH1 adsorption state to the atomic adsorption of two oxygen atoms at two neighboring hollow sites. The energy barriers of O$_{2}$ on different Pb(111) films are found to be modulated by the QSE of Pb(111) films, and show a bilayer oscillation behavior. Our study further complete the theoretical picture for the adsorption and dissociation of O$_{2}$ molecules on different Pb(111) films. This work was supported by the NSFC under grants No. 10604010, 10904004, and 60776063. ∗ Corresponding author; zhang ping@iapcm.ac.cn (P.Z.). 1 Busnengo, H. F.; Salin, A.; Dong, W. J. Chem. Phys. 2000 , 112 , 7641; Rivi` ere, P.; Salin, A.; Mart´ın, F. J. Chem. Phys. 2006 , 124 , 084706. 2 Kung, H. H. Transition Metal Oxides, Surface Chemistry and Catalysis ; Elsevier: Amsterdam, 1989; Henrich, V. E.; Cox, P. A. The Surface Science of Metal Oxides ; Cambridge University Press: Cambridge, 1994. 3 BGLYPH<suppress>lo´ nski, P.; Kiejna, A.; Hafner, J. Phys. Rev. B 2008 , 77 , 155424. 4 Yotsuhashi, S.; Yamada, Y.; Kishi, T.; Di˜ no, W. A.; Nakanishi, H.; Kasai, H. Phys. Rev. B 2008 , 77 , 115413. 10