▎ 摘　　要

Time-dependent density functional theory (TDDFT) within the random phase approximation (RPA) is used to obtain the time evolution of the induced potential produce by the sudden formation of a C 1s core hole inside a graphene monolayer, and to show how the system reaches the equilibrium potential. The characteristic oscillations in the time-dependent screening potential are related to the excitations of pi and sigma + pi plasmons as well as the low energy 2D plasmons in doped graphene. The equilibrium RPA screened potential is compared with the DFT effective potential, yielding good qualitative agreement. The self energy of a point charge near a graphene monolayer is shown to demonstrate an image potential type behavior, Ze/(z - z(0)), down to very short distances (4 a.u.) above the graphene layer. Both results are found to agree near quantitatively with the DFT ground state energy shift of a Li+ ion placed near a graphene monolayer.