The 5-parameter Morse potential (for short 5-MP) of the interaction between C, 0 atom and Rh surface and the extended LEPS potential have been constructed, and the adsorption and diffusion of CO molecules on Rh low index surfaces and open rough Rh(331) stepped surface are investigated. This work puts forward the concept of vibration dactylogram property for molecular adsorption states. The calculation results and the analysis of vibration dactylogram show that there exists the commonness in the adsorption on Rh low index surfaces and Rh(331) stepped surface: with the increasing coverage, the top, bridge sites are adsorbed in perpendicularly in sequence, and the top sites are the steady adsorption sites and the bridge sites are the next. On (100) surface, CO molecules obtain the eigenvibration of 2009, 1946 cm-1 on the top and bridge sites respectively and the difference between the binding energy of above two sites is 0.09 eV; on (110) surface, CO molecules obtain the eigenvibration of 2019, 1961 cm-1 respectively; on (111) surface, CO molecules on the top, bridge and hollow sites produce the eigenvibration of 2000, 1912, 1894 cm-1 respectively, the binding energies of the three sites decrease in tum and the discrepancy between the top and bridge sites is 0.03 eV; on (331) surface, top and bridge sites between two equivalent top sites are adsorbed in, and then obtain the eigenvibration of2018, 1987 cm-\ 1969, 1927 cm-1 respectively.The adsorption of carbon monoxide on single-crystal transition metal surfaces has received considerable attention by the surface science community. Not only can the chemisorption of CO on a metal surface be regarded as a model adsorption system but also its industrial importance is great in such areas as the catalysis of CO hydrogenation to produce hydrocarbons and of CO oxidation in controlling automobile exhaust [l]. The bonding of carbon monoxide to Rh is of special interest since this metal catalyzes the hydrogenation of CO in both heterogeneous and homogeneous media [2]. However, the adsorption and oxidation properties of CO at Rh surface have received much interest in the past, and with the increasing use of Rh as a component of the car exhaust catalyst, further interest has 1012 been recently simulated [3]. The scientists have adopted low energy electron diffraction, electron energy loss spectroscopy, infrared reflection absorption spectroscopy, etc. to perform the effective research, but the theoretical studies about this system are rare.For (100) surface, the researchers consider that top sites are adsorbed in at low coverage, and top and bridge sites will be occupied with increasing coverage. Of course, there are different viewpoints. Leung[4] et aI. assigned their obtained IRAS spectra to top, bridge sites, and point out explicitly the diversity of the binding energy between top and bridge sites is 0.1-0.4 kcal/mol and the bridge sites are the more stable species. Chang[5] et al. educed that bridge sites are adsorbed in firstly and then the top sites. Due to the complexity o...