  We generalize the recently developped "internal" Density Functional Theory
(DFT) and Kohn-Sham scheme to multicomponent systems. We obtain a general
formalism, applicable for the description of multicomponent self-bound systems
(as molecules where the nuclei are treated explicitely, atomic nuclei and mix
of 3He and 4He droplets), where the fundamental translational symmetry has been
treated correctly. The main difference with traditional DFT is the explicit
inclusion of center-of-mass correlations in the functional. A large part of the
paper is dedicated to the application to molecules, which permits among other
to clarify the approximations that underly traditional DFT.
