Optical absorption spectrum of Ce@C$_{82 }$

Optical absorption spectrum for the Ce@C$_{82}$ endohedral fullerene has been studied using the density-functional theory and the many-body Green's-function approaches. Geometry optimization was performed using the DMol$_{3 }$software. A plane wave approach as implemented in the ABINIT$_{ }$Package has been used to solve the Kohn-Sham equation. Self-energy was evaluated by the GW approximation, which is the product of one-electron Green's function G$_{0 }$ and screened Coulomb interaction W$_{0.}$ Finally the optical absorption spectra have been calculated using the random phase approximation (RPA), RPA plus self-energy correction (RPA-GW) and the Bethe-Salpeter equation (BSE-GW).