Adsorption of polar monomers on ice surface, relevant to the physical/chemical reaction in ice clouds as well as growth of ice, remains an open issue partially due to the unusual surface characteristics with protons at the top layer of ice. Using first-principle calculations, we explore the adsorption properties of ice surface in terms of a surface proton order parameter, which characterizes the inhomogeneity of the dangling atoms on ice surface. We show that, due to an effective electric field created by dangling OH bonds and lone pairs of water molecules not only directly neighboring but also further away from the adsorbed polar molecule on the ice surface, the adsorption energy of polar monomer on ice surface exhibits large variance and a strong correlation with the proton order parameter of ice surface. Our results about the positive correlation between the inhomogeneity of ice surface and adsorption energies suggest that the physical/chemical reactions as well as the growth of ice may prefer to occur firstly on surfaces with larger proton order parameter.surface science | ice basal surface | ice growth | ice basal plane I ce, one of the most abundant materials on earth, plays an important role in interstellar phenomena, life in the cryosphere and global climate (1-3). Adsorption on ice surface, especially hexagonal ice, is related to the fundamental question of how ice particles grow into hexagonal ice crystal or snow flakes, and what kind of roles it plays for the reactive and catalytic properties of atmospheric ice associated with environment-related issues (1-4). For instance, the ice surface acts as a catalyst in heterogeneous physical/chemical reactions leading to the destruction of ozone (5). It has long been recognized that the adsorption properties depend on the structure of the ice surface (6-9). However, it is still striking to see that many properties of ice surfaces vary greatly even on a prefect ice surface where the oxygen atoms are ordered in a hexagonal lattice (10-13). Yet, due to the complexity of the surface structure at the atomic level, our understandings of the activity and adsorption property on the ice surface are still far from consistent and complete.At interfaces, the Bernal-Fowler-Pauling ice rule (14, 15) cannot be obeyed; that is, nearest neighboring water molecules cannot satisfy all hydrogen bonds, thus forming dangling protons and lone pairs. Recent works (16-18) have shown that the inhomogeneity of dangling atoms, which can be characterized by a proton order parameter (17), is important for the energies of water ice surfaces (17,18). This order parameter, C OH , characterizing the arrangement of dangling OH bonds on the ice surface (17), is defined aswhere N OH is the total number of dangling OH bonds on the surface and c i is the number of the nearest neighboring dangling OH bonds around the ith OH bond. For the ice slab without dipole moment perpendicular to the surface, the order parameter ranges from 2 to 6 (17). We note that the most ordered dangling OH distribution on...