Quantal Density Functional Theory of Degenerate States

The treatment of degenerate states within Kohn-Sham density functional theory (KS-DFT) is a problem of longstanding interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory (Q-DFT). We describe the Q-DFT of \textit{both} ground and excited degenerate states, and for the cases of \textit{both} pure state and ensemble v-representable densities. This then further provides a rigorous physical interpretation of the density and bidensity energy functionals, and of their functional derivatives, of the corresponding KS-DFT. We conclude with examples of the mappings within Q-DFT.