A problem on a dimer adsorbed at single-sheet graphene

In the context of the previously proposed M model for the density of states in graphene (Davydov and Sabirova [3]), two adatoms coupled via the amplitude of electron transitions from one adatom to the other (direct exchange) are considered. An analytical expression for the energy density of states in/for the dimer is derived, and the dependence of the charge of the dimer’s constituent atoms on the parameters of the problem is analyzed. The effect of image forces is investigated. In the context of the surface molecule model, a dimer composed of hydrogen adatoms is considered. The dissociation and desorption energies of such a dimer are estimated.