Uniqueness of the density-to-potential mapping in excited-state density-functional theory

References: Fig.1: Two potentials (middle panel) giving the same excited-state density (upper panel) along with their corresponding ground-state densities (lower panel) for an excited-state of the three electron 1D infinitely deep well model system. The question of whether there exists a mapping from an excited-state density to a potential is central to performing density-functional calculation for excited states. The motivation of the present work is to establish a unique way of selecting a system (potential) for a given excited-state density. The issue of density – to – potential mapping has been addressed in a series of work by Sahni et al [1], Harbola [2] and Gaudoin et al [3]. In the work of [1] and [2], it was shown that groundor excited-state density can be generated by configuration of one’s choice. In the work [3], they have shown that even with a fixed configuration, one could reproduce same excited-state density from more than one potentials as shown in Fig.1. This implies in addition to the excited-state density one requires some extra information to establish such a unique mapping. This has been done by comparison of ground state densities in Levy-Nagy [4] theory. Following the earlier attempts we have further explored the density-topotential mapping based on the work of Levy-Nagy [4] and Gorling [5] for excited-states [6]. We have proposed a new criterion [7], which uniquely establishes such mapping. [1] V. Sahni, L. Massa, R. Singh and M. Slamet, Phys. Rev. Lett. 87, 113002 (2001). [2] M. K. Harbola, Phys. Rev. A 69, 042512 (2004). [3] R. Gaudoin and K. Burke, Phys. Rev. Lett. 93, 173001 (2004). [4] M. Levy and A. Nagy, Phys. Rev. Lett. 83, 4361 (1999). [5] A. Gorling, Phys. Rev. A 59, 3359 (1999). [6] P. Samal, M. K. Harbola and A. Holas, Chem. Phys. Lett. 419, 217 (2006) [7] P. Samal and M. K. Harbola, J. Phys. B 39, 4065 (2006).