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Long-timescale simulations of the diffusion of a H$_2$O admolecule on the(0001) basal plane of ice Ih were carried out over a temperature range of 100to 200 K using the adaptive kinetic Monte Carlo method and TIP4P/2005finteraction potential function. The arrangement of dangling H atoms was variedfrom the proton-disordered surface to the perfectly ordered Fletcher surface. Alarge variety of sites was found leading to a broad distribution in adsorptionenergy at both types of surfaces. Up to 4 % of the sites on theproton-disordered surface have an adsorption energy exceeding the cohesiveenergy of ice Ih. The mean squared displacement of a simulated trajectory at175 K for the proton-disordered surface gave a diffusion constant of6$\cdot$10$^{-10}$ cm$^2$/s, consistent with an upper bound previously reportedfrom experimental measurements. During the simulation, dangling H atoms werefound to rearrange so as to reduce clustering, thereby approaching a linearFletcher type arrangement. Diffusion on the perfectly ordered Fletcher surfacewas estimated to be significantly faster, especially in the direction along therows of dangling hydrogen atoms. From simulations over the range intemperature, an effective activation energy of diffusion was estimated to be0.16 eV and 0.22 eV for diffusion parallel and perpendicular to the rows,respectively. Even a slight disruption of the rows of the Fletcher surface madethe diffusion isotropic.

Long-timescale simulations of H$_2$O admolecule diffusion on Ice Ih(0001) surfaces