3 for the O$_{2}$ dissociation on sp metal surfaces. Motivated by these backgrounds, in this paper we investigate the dissociation of O$_{2}$ molecules on another sp metal surface, lead (Pb). We find that the adiabatic DFT calculation also leads to reliable results for the O$_{2}$/Pb(111) system. Another motive for us to study the O$_{2}$ dissociation on the Pb(111) surface is that atom- ically uniform Pb films with thickness from several to tens of monolayers (MLs) have been successfully fabricated on both metal and semiconductor substrates $^{20,21}$, which can serve as an ideal prototype for experimental researchers to investigate the surface oxidation of Pb. However, it is believed that for very thin metal films, the adsorption and dissociation of O$_{2}$ molecules becomes more complex because of the two boundaries. According to the “particle- in-a-box” model, electrons confined in a uniform film are quantized into discrete energy levels along the film-normal direction, forming the so-called quantum well states. Because the elec- tron Fermi wavelength of Pb is nearly 4 times the lattice spacing along the [111] direction $^{22}$, many properties like thermal stability, surface energy, and work function of the Pb films oscillate with thickness with a quasibilayer period $^{23–25}$. Recently, a unique two-step method has been brought out to efficiently oxidize the the Pb(111) surface $^{26,27}$. During this special oxidation process, O$_{2}$ molecules are firstly introduced at a low temperature and adsorb in a precursor state, then the Pb(111) surface is oxidized by a subsequently annealing to room temperature $^{27}$. Most interestingly, both the oxygen coverage at low temperature and oxide coverage after annealing are found to be modulated by the quantum size effect (QSE) of ultrathin Pb(111) films $^{26}$. These studies together with other investigations28 clearly prove the modulation of surface oxidation by QSE. To understand the complicated experimen- tal observations, the systematical investigations on the adsorption and dissociation of O$_{2}$ molecules on ultrathin Pb(111) films are needed. In our previous work, we have already studied the adsorption properties for both molec- ular O$_{2}$ and atomic O on different Pb(111) films $^{29,30}$. It is found that O$_{2}$ molecules will not spontaneously dissociate on Pb(111) films, and a precursor molecular adsorption state exists $^{29}$. Here in this work, we further analyze the electronic interactions for the adsorption of O$_{2}$, investigate the dissociation process for O$_{2}$, and study the QSE on the dissociation energy barriers. The rest of the paper organized as follows. In Sec. II, we give details of the first-principles total energy calculations, which is followed in Sec. III by our analysis for the adsorption state of O$_{2}$ on the Pb(111) surface. In Sec. IV, we study the O$_{2}$ dissociation