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Demonstration that the proton ordering COH affects the adsorption energy of ice surface. Approximately, the larger the order parameter (the more inhomogenous the ice surface) is, the higher the adsorption energy. There exists a large variation in the adsorption energy for a fixed order parameter, among which the largest adsorption energy is lower than the bulk cohesive energy (dashed line) for COH < 2.5 but higher than the bulk cohesive energy for COH > 2.5.
