▎ 摘　　要

The electronic structure of selected rare-earth atoms adsorbed on a free-standing graphene was investigated using methods beyond the conventional density functional theory (DFT+U, DFT+HIA, and DFT+ED). The influence of the electron correlations and the spin-orbit coupling on the magnetic properties has been examined. The DFT+U method predicts both atoms to carry local magnetic moments (spin and orbital) contrary to a nonmagnetic f(6) (J = 0) ground-state configuration of Sm in the gas phase. Application of DFT+Hubbard-I (HIA) and DFT+exact diagonalization (ED) methods cures this problem, and yields a nonmagnetic ground state with six f electrons and J = 0 for the Sm adatom. Our calculations show that Nd adatom remains magnetic, with four localized f electrons and J = 4.0. These conclusions could be verified by STM and XAS experiments.