Building Kohn-Sham potentials for ground and excited states

Abstract

We analyze the inverse problem of Density Functional Theory using a regularized variational method. First, we show that given $k$ and a target density $\rho$, there exist potentials having $k^{\text{th}}$ bound mixed states which densities are arbitrarily close to $\rho$. The state can be chosen pure in dimension $d=1$ and without interactions, and we provide numerical and theoretical evidence consistently leading us to conjecture that the same pure representability result holds for $d=2$, but that the set of pure-state $v$-representable densities is not dense for $d=3$. Finally, we present an inversion algorithm taking into account degeneracies, removing the generic blocking behavior of standard ones.

References in corpus (3)

• Geometric methods for nonlinear many-body quantum systems
• Kohn-Sham calculations with the exact functional
• Some properties of the potential-to-ground state map in quantum mechanics

Cited by in corpus (14)

• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Exact Excited-State Functionals of the Asymmetric Hubbard Dimer
• Seven Useful Questions in Density Functional Theory
• Ensemble density functional theory of ground and excited energy levels
• Density-potential inversion from Moreau-Yosida regularization
• Some properties of the potential-to-ground state map in quantum mechanics
• Geometry of Degeneracy in Potential and Density Space
• Nuclear energy density functionals from empirical ground-state densities
• Solution of the v-representability problem on a one-dimensional torus
• Excited-State-Specific Kohn-Sham Formalism for the Asymmetric Hubbard Dimer
• Excited States of the Uniform Electron Gas
• Exact static linear response of excited states from ensemble density functional theory
• The complete inverse Kohn-Sham problem: from the density to the energy
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory