  We develop a scheme for building the scalar exchange-correlation (xc) kernel
of time-dependent density functional theory (TDDFT) from the tensorial kernel
of time-dependent {\em current} density functional theory (TDCDFT) and the
Kohn-Sham current density response function. Resorting to the local
approximation to the kernel of TDCDFT results in a nonlocal approximation to
the kernel of TDDFT, which is free of the contradictions that plague the
standard local density approximation (LDA) to TDDFT. As an application of this
general scheme, we calculate the dynamical xc contribution to the stopping
power of electron liquids for slow ions to find that our results are in
considerably better agreement with experiment than those obtained using TDDFT
in the conventional LDA.
