Density-to-potential map in time-independent excited-state density-functional theory

TL;DR

This paper investigates the uniqueness of the density-to-potential mapping in time-independent excited-state density-functional theory, suggesting that the Levy-Nagy criterion may ensure a one-to-one correspondence.

Contribution

It provides a quantitative analysis of the Levy-Nagy criterion's role in establishing a unique density-to-potential map for excited states.

Findings

Levy-Nagy criterion may ensure unique density-potential mapping

Quantitative analysis supports the criterion's effectiveness

Focus on excited-state density-functional theory

Abstract

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.