  Superconductivity in intercalated graphite CaC6 and H under extreme pressure,
in the framework of superconducting density functional theory, is discussed. A
detailed analysis on how the electron-phonon and electron-electron interactions
combine together to determine the superconducting gap and critical temperature
of these systems is presented. In particular, we discuss the effect on the
calculated Tc of the anisotropy of the electron-phonon interaction and of the
different approximations for screening the Coulomb repulsion. These results
contribute to the understanding of multigap and anisotropic superconductivity,
which has received a lot of attention since the discovery of MgB2, and show how
it is possible to describe the superconducting properties of real materials on
a fully ab-initio basis.
