Building Kohn-Sham potentials for ground and excited states

• URL: http://arxiv.org/abs/2101.01127v2
• Date: Thu, 30 Jun 2022 12:11:08 GMT
• Title: Building Kohn-Sham potentials for ground and excited states
• Authors: Louis Garrigue
• Abstract summary: We show that given $k$ and a target density $rho$, there exist potentials having $ktextth$ bound mixed states which densities are arbitrarily close to $rho$. We present an inversion algorithm taking into account degeneracies, removing the generic blocking behavior of standard ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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