TDDFT extends the concept of stationary DFT
to time-dependent situations:
For any interacting quantum many-particle system subject to a given
time-dependent potential all physical observables are uniquely
determined by knowledge of the time-dependent density and the state
of the system at an arbitrary, single instant in time [1].
In particular, if the time-dependent potential is switched on at some
time $t$_{0} and the system has been in its ground state
until $t$_{0}, all observables are unique functionals of
only the density: In this case the initial state of the system at
time $t$_{0} is a unique functional of the density at
$t$_{0}, which is identical with the ground state density
of the stationary system one has before $t$_{0}
(for all times until $t$_{0} the one-to-one correspondence
is guaranteed by the Hohenberg-Kohn theorem for stationary systems).
This unique relationship allows to derive a calculational scheme in
which the effect of the particle-particle interaction is represented
by a density-dependent single-particle potential, so that the time
evolution of an interacting system can be studied by solving a
time-dependent auxiliary single-particle problem.
Additional simplifications are obtained in the linear response
regime [2].
Like in stationary DFT the major task of TDDFT is to find suitable
approximations for the exchange-correlation (xc) part of the
effective single-particle potential.

In our group the TDDFT approach has been applied to the
photo absorption of metal clusters
using both the time-dependent local density approximation [3,4]
and the exact exchange (on the basis of the
optimized-potential-method [5]) as approximations for the
effective xc-potential.
In particular, we have developed an adiabatic linear response type
approximation to the full time-dependent optimized-potential-method
[6].