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.