Density-to-potential map in time-independent excited-state   density-functional theory
  In light of the recent work by Sahni et al., Harbola, and Gaudoin and Burke, the question of mapping from an excited-state density of a many-electron interacting system to the potential of the related non-interacting system is analyzed. To do so, we investigate the Levy-Nagy criterion quantitatively for several excited-states. Our work indicates that Levy-Nagy criterion may fix the density to potential map uniquely. 
Prasanjit Samal, Manoj K. Harbola and A. Holas