a Both adsorption and dissociation of the diatomic molecular NO on Pd (100) and (111) surfaces are studied using the extended London-Eyring-Polyani-Sato (LEPS) method constructed by means of 5-MP (the 5-parameter Morse potential). All critical characteristics of the system that we obtain, such as adsorption geometry, binding energy, eigenvalues for vibration, are in good agreement with the experimental results. On Pd (100) surface, NO prefers to adsorb in fourfold hollow site (H) uprightly at low coverage. With increase in the coverage NO gradually tilts in fourfold hollow and bridge sites. For NO-Pd (111) system, two adsorption states are found at low coverage, of which one adsorption state is the B(tilt) state that the centroid of NO projects at bridge site, another (H-B-H state) that NO almost parallels to the (111) surface with the vibration frequency of 610 cm −1 , but the frequency is near to that of the atoms, which is easy to be ignored in experiments. At high coverage, two transitional states (BH and HT) are found. NO is difficult to dissociate on Pd (100) and (111) surfaces. Especially for NO-Pd (111) system, the three-well-potential dissociation mode is initially put forward to show the remarkable dissociation process with two dissociation transitional states of NO on Pd (111).