Propagation of initially excited states in time-dependent density-functional theory

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, discuss different valid choices of the initial Kohn-Sham state, and explore the errors inherent in the adiabatic approximation that neglects this dependence.