  The exact exchange-correlation (xc) potential of time-dependent density
functional theory has been shown to have striking features. For example, step
and peak features are generically found when the system is far from its
ground-state, and these depend nonlocally on the density in space and time. We
analyze the xc potential by decomposing it into kinetic and interaction
potential components, and comparing each with their exact-adiabatic
counterparts, for a range of dynamical situations in model one-dimensional (1D)
two-electron systems. We find that often, but not always, the kinetic contri-
bution is mostly responsible for these features, that are missed by the
adiabatic approximation. The adiabatic approximation often makes a smaller
error for the potential contribution, which we write in two parts, one being
the Coulomb potential due to the time-dependent xc hole. These observations
also held in non-equilibrium cases we studied where there are large features in
the correlation po- tential although no step structure. In ground-state
situations, step and peak structures arise in cases of static correlation, when
more than one determinant is essential to describe the interacting state. We
investigate the time-dependent natural orbital occupation numbers and find the
corresponding relation between these and the dynamical step is more complex
than for the ground-state case.
