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Adsorption and surface coverage of CO on the Ru(0001)and the adsorption of H2 on nCO-covered Ru(0001)have been computed at the density functional theory(DFT)level under the consideration of the temperature,CO and H2 partial pressure by using an ab initio atomistic thermodynamics method.On the basis of the computed Gibbs free energies,the relationship between CO coverage on the Ru(0001)surface and temperature as well as CO partial pressure has been established.The computed phase diagram,which is basic consistent with the experimental value,shows that a stable CO coverage can be obtained within a range of temperature and partial pressure.And it is possible to adjust the balance between temperature and CO partial pressure for practical uses and to identify the initial states and the active sites under given conditions.Then the adsorption of H2 on nCO-covered Ru(0001)are explored(n= 1-12),because saturated CO coverage has 12 CO.The most stable adsorption sites at different coverage of H2 on nCO-covered Ru(0001)have been found,and we get the saturated monolayer coverage of H2 on nCO-covered Ru(0001).With the coverage of CO increases,the saturated monolayer coverage of H2 decreases.We find that H2 does not adsorb on the surface with more than 7 CO.The saturated adsorption has 7 H2 molecules on 1CO-covered Ru(0001),6 H2 molecules on 2CO-covered Ru(0001),5 H2 molecules on 3 and 4CO-covered Ru(0001),3 H2 molecules on 5CO-covered Ru(0001),and 1 H2 molecules on 6CO-covered Ru(0001).In order to getting a initial information of H2 coverage on the nCO-covered Ru(0001)surface at a given experimental conditions,we introduced the influence of temperature and H2 partial pressure(pH2)by applying atomistic thermodynamics methods,as well.In addition,we validate our methods and models reasonably by comparing with experimental value.In a word,we find a reliable method to probe into the stable H2 coverage corresponding to different pH2/pCO,on a fixed coverage of CO and temperature.