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, and explore the errors inherent in the adiabatic approximation that neglect this dependence.