Models for diffusion and Island growth of hydrogen on graphene

A Hydrogen atom can either physisorb or chemisorb on a graphene surface. A model for the diffusion of a hydrogen atom, between nearest neighbor chemisorption sites on graphene surface, is presented. The parameters of the model are optimized against a full set of barriers obtained from the first principles. The energy barrier of the hopping hydrogen is related to the local environment of the hopping hydrogen. In model I, the local environment of the migrating hydrogen include four sites (or 24 configurations). Depending on whether these sites are occupied or empty a total of sixteen configurations (barriers) are required to be calculated. Due to symmetry, only 10 of these configurations are independent. In model II, the local environment of the migrating hydrogen include eight sites (28 configurations). Out of these 256 configurations, a little more than half of them are independent. Models I and II have three and four parameters, respectively. The parameters of the two models are obtained by fitting the barriers to the corresponding ones from the Quantum Espresso code. The comparisons between the models and the first principles would serve as a gauge as to whether extension to a larger local environment is warranted.