Developments in excited-state density functional theory

This article discusses the reasons behind the apparent lack of success of density functional theory (DFT), during the past three decades, with excited states of many-electron systems. It describes various variational and non-variational approaches developed so far for dealing with this problem. Those include Theophilou's equiensemble approach, extended to unequally weighted ensembles by Gross et al., Fritsche's wavefunction partitioning approach, local scaling transformation theory by Kryachko et al., the work-function formalism developed by Harbola and Sahni, etc. Through intimate connections between time-dependence and excited states, under a perturbation, various time-dependent (TD) DFT approaches to excited states, e.g., a quantum fluid dynamical approach, a TD density-functional response theory and a TD optimized effective potential approach, are also reviewed