Model of adsorption on graphene

A simple M-shaped model has been proposed for the density of states of the π bands of the graphene. The model has been used to derive the expression for the local density of states on the adsorbed atom and to calculate the corresponding occupation numbers for different model parameters. Additional simplifications have made it possible to represent the band contribution n _b to the total occupation number of the adatom n _a in the analytical form. The contributions of local states n _l to n _a = n _b + n _l have been calculated for different parameters. The charge has been numerically evaluated for the case of adsorption of alkali metal atoms on the graphene. The results obtained have been verified using the model of a surface diatomic molecule calculated by the Harrison bond-orbital method. The verification has demonstrated that the charges calculated in terms of radically different models are in good agreement.