Transition metal and rare-earth metal atoms on single-layer graphene: Estimations of the charge transfer and adsorption energy

A Hamiltonian accounting for $s$- and $d(f)$-states of adatoms has been proposed to describe adsorption of atoms of $d$- and $f$-metals on single-sheet graphene. It has been shown that s-electrons mainly contribute to the charge transfer $\Delta n_a$ between the adatom and graphene substrate. Analytical formulas proposed previously within the $M$-model of the graphene density of states are used for $\Delta n_a$ calculations. To estimate the adsorption energy, a simple analytical expression is proposed. Calculations are performed for 3$d$-, 4$d$-, 5$d$-, and 4$f$-adatoms. The results of calculations are compared with the data obtained by other authors.