  The Kohn-Sham approach to time-dependent density-functional theory (TDDFT)
can be formulated, in principle exactly, by invoking the force-balance equation
for the density, which leads to an explicit expression for the
exchange-correlation potential as an implicit density functional. It is shown
that this suggests a reformulation of TDDFT in terms of the second time
derivative of the density, rather than the density itself. The result is a
time-local Kohn-Sham scheme of second order in time whose causal structure is
more transparent than that of the usual Kohn-Sham formalism. The scheme can be
used to construct new approximations at the exchange-only level and beyond, and
it offers a straightforward definition of the exact adiabatic approximation.
