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 turn 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 of 2018, 1987 cm(-1); 1969, 1927 cm(-1) respectively.