  Many recent applications of time-dependent density functional theory begin in
an initially excited state, and propagate it using an adiabatic approximation
for the exchange-correlation potential. This however inserts the excited-state
density into a ground-state approximation. By studying a series of model
calculations, we highlight the relevance of initial-state dependence of the
exact functional when starting in an excited state, and explore the errors
inherent in the adiabatic approximation that neglect this dependence.
