Controlling the contact angles of the wettability is an important issue especially in industrial applications. Establishing its {it ab initio} predictions is hence a topic of great interest. For the predictions, it is required to setup a model of the adsorption structure of liquid molecules on a surface. The appropriate setting is expected to depend on whether the surface is of insulating or metallic materials, the latter of which is the target of the present study while all preceding {it ab initio} studies have worked on the former. Since the feasibility of {it ab initio} evaluations relies on the approximation of the liquid-gas interface energy evaluated roughly by the crystal ice, it would be a natural choice to take the periodic honeycomb array of the water molecules as the adsorbing model of water on the surface. Although the periodic model have successfully been used for the preceding treatments of insulating surfaces, we found for the case with metallic surfaces that the periodic model gives worse prediction to reproduce experimental values. Rather than that, the models with isolated water multimers are found to give better predictions. The ambiguity of the models about the size of multimers and the coverage is found to be small ($simpm 10^{circ}$), and is averaged over to give a plausible value based on the Boltzmann weight with the adsorbing energies. The procedure we are providing can generally be applicable to any of wettability on the surfaces of metallic materials.
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