Lack of Hohenberg-Kohn theorem for excited states.

@article{Gaudoin2004LackOH,
  title={Lack of Hohenberg-Kohn theorem for excited states.},
  author={R. Gaudoin and Karen M. Burke},
  journal={Physical review letters},
  year={2004},
  volume={93 17},
  pages={
          173001
        }
}
For a given excited state there exist densities that arise from more than one external potential. This is due to a qualitatively different energy-density relationship from that of the ground state and is related to positive eigenvalues in the nonlocal susceptibility for excited states. Resulting problems with the generalization of the density functional methodology to excited states are discussed. 

Figures from this paper

Building Kohn–Sham Potentials for Ground and Excited States
  • Louis Garrigue
  • Mathematics
    Archive for Rational Mechanics and Analysis
  • 2022
. We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given k and a target density ρ , there exist potentials having k th excited
Exploring foundations of time-independent density functional theory for excited states
Based on the work of Gorling and that of Levy and Nagy, a density-functional formalism for many fermionic excited states is explored through a careful and rigorous analysis of the excited-state
Time-independent excited-state density functional theory: study of 1s22p3(4S) and 1s22p3(2D) states of the boron isoelectronic series up to Ne5+
Using accurate Monte Carlo densities for excited states of the boron isoelectronic series, we construct the Kohn–Sham systems for these excited states. The Kohn–Sham system is that for which the
Some Properties of the Potential-to-Ground State Map in Quantum Mechanics
We analyze the map from potentials to the ground state in static many-body quantum mechanics. We first prove that the space of binding potentials is path-connected. Then we show that the map is
Rydberg energies using excited state density functional theory.
TLDR
It is found that eDFT plays a complementary role to constrained DFT: the former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.
Vertical excitation energies from the adiabatic connection.
  • A. Becke
  • Physics
    The Journal of chemical physics
  • 2016
TLDR
This work uses the "adiabatic connection" to analyse the role of the two-electron integrals, obtaining a time-independent DFT approach to excitation-energy calculations that is new and simple.
Local effective potential theory: nonuniqueness of potential and wave function.
TLDR
There is an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system and the authors show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function.
Electronic excitations through the prism of mean-field decomposition techniques.
The potential of mean-field decomposition techniques in interpreting electronic transitions in molecules is explored, in particular, the usefulness of these for offering computational signatures of
...
...