Exact time-dependent density-functional theory for nonperturbative dynamics of the helium atom

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist for real three-dimensional systems. We demonstrate that the Kohn-Sham and true current densities differ by a rotational component. The results have direct implications for approximate time-dependent density functional theory calculations of atoms and molecules in strong fields, emphasizing the need to go beyond the adiabatic approximation, and highlighting caution in the quantitative use of the Kohn-Sham current.