  We generalize to the time-dependent case the stationary Internal DFT /
Kohn-Sham formalism presented in Ref. [14]. We prove that, in the
time-dependent case, the internal properties of a self-bound system (as an
atomic nuclei) are all defined by the internal one-body density and the initial
state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way
to compute the internal density. The main difference with the traditional DFT /
Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the
functional.
