We analysed the H/D isotope effect of CH4/CD4adsorption on a Rh(111) surface using our combined plane wave and localized basis sets method, that we proposed for the consideration of delocalized electrons on a surface and the quantum effect of protons (deuterons) in metal-molecule interactions. We observed that the adsorption distance and energy of CD4were larger and lower than those of CH4, respectively. This is in reasonable agreement with the corresponding experimental results of cyclohexane adsorption. We clearly found that the trend of the H/D isotope effect in the geometrical and energetic difference was similar to that of the hydrogen-bonded systems.