  We have recently put forward a steady-state density functional theory (i-DFT)
to calculate the transport coefficients of quantum junctions. Within i-DFT it
is possible to obtain the steady density on and the steady current through an
interacting junction using a fictitious noninteracting junction subject to an
effective gate and bias potential. In this work we extend i-DFT to the time
domain for the single-impurity Anderson model. By a reverse engineering
procedure we extract the exchange-correlation (xc) potential and xc bias at
temperatures above the Kondo temperature $T_{\rm K}$. The derivation is based
on a generalization of a recent paper by Dittmann et al. [arXiv:1706.04547].
Interestingly the time-dependent (TD) i-DFT potentials depend on the system's
history only through the first time-derivative of the density. We perform
numerical simulations of the early transient current and investigate the role
of the history dependence. We also empirically extend the history-dependent TD
i-DFT potentials to temperatures below $T_{\rm K}$. For this purpose we use a
recently proposed parametrization of the i-DFT potentials which yields highly
accurate results in the steady state.
