Building KohnSham 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 $k^{\text{th}}$ excited 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 potentialrepresentable pure state densities is not dense for $d=3$. Finally, we present an inversion algorithm taking into account degeneracies.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2101.01127
 Bibcode:
 2021arXiv210101127G
 Keywords:

 Mathematical Physics;
 Condensed Matter  Materials Science;
 Physics  Chemical Physics;
 Quantum Physics