Cluster expansion method for adsorption: Application to hydrogen chemisorption on graphene

A systematic method is presented for determining the ground state of absorbed species on a substrate based on a cluster expansion of the configurational energy. It is shown that the method can determine the ground state of a strongly relaxing system using a few first-principles total energy calculations of small cells only. The method is applied to a particularly challenging case, the two-sided hydrogen chemisorption on a free standing graphene sheet, where, as a function of hydrogen coverage, the carbon hybridization goes from ${\mathrm{sp}}^2$ to ${\mathrm{sp}}^3.$ The method should require still fewer calculations and yield still more accurate results in the case of physisorption where longer-ranged strain effects are less important.