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 sp(2) to 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.