The extended LEPS constructed by 5-MP (the 5-parameter Morse potential) is performed. At low coverage, O-2 prefers to dissociate on the Pd(100) and (110) surfaces; however, at high coverage, it can stably adsorb in the H-B-H site on the Pd(111) surface and more molecular states are found. The calculation results agree well with the experimental results, especially, the results of O-2 on Pd(111) explain well the three precursor states (the superoxo-like state, the peroxo-like and second peroxo-like state) of HREELS and EELS results. Simultaneously, the conceptions of the molecular dissociation limit and the surface dissociation distance are brought forward first, which illuminate the dissociation mechanism of the O-2 on the low-index surfaces and offer the answer to the question why is it more difficult for O-2 to dissociate on the (111) surface than on the (100) and (110) surfaces?