  Using the Runge-Gross theorem that establishes the foundation of
Time-dependent Density Functional Theory (TDDFT) we prove that for a given
electronic Hamiltonian, choice of initial state, and choice of fragmentation,
there is a unique single-particle potential (dubbed time-dependent partition
potential) which, when added to each of the pre-selected fragment potentials,
forces the fragment densities to evolve in such a way that their sum equals the
exact molecular density at all times. This uniqueness theorem suggests new ways
of computing time-dependent properties of electronic systems via fragment-TDDFT
calculations. We derive a formally exact relationship between the partition
potential and the total density, and illustrate our approach on a simple model
system for binary fragmentation in a laser field.
