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Vibrational properties of hydrogen on the Rh(111) surface have been investigated theoretically. The potential energy surface for this system has been calculated within the density functional theory. The potential is found to be very anharmonic. The wave functions and their energies for the hydrogen motion on the potential energy surface (PES) have been calculated and assigned by using discrete variable representation. It was found that the vibrational wave function is localized at hollow site in the ground state for hydrogen on Rh(111). Higher excited states are of delocalized nature and mixed parallel and perpendicular character. Our results are in good agreement with the observed vibrational spectra of hydrogen on the Rh(111) surface.