  Hydrogen adatoms induced magnetic moment on graphene has been observed in
atomic scale in a recent experiment [Gonzalez-Herrero et al., Science 352, 437
(2016)]. Here, we demonstrate that all the experimental phenomena can be simply
and well described by an equivalent Anderson impurity model, where the
electronic correlations on both carbon and hydrogen atoms are represented by an
effective on-site Coulomb interaction on hydrogen adatom $U_H$. This simple
equivalent model works so well is because that the main effect of Coulomb
interaction on both carbon and hydrogen atoms is just to split the impurity
resonance states with different spin. This effective Anderson impurity model
can also well reproduce all the behaviours of hydrogen dimer on graphene
observed in experiment. We thus argue that it should be a general model to
describe the hydrogen adatoms on graphene with various adsorption
configurations, especially for their magnetic properties.
