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Preprints, Working Papers, ... Year : 2021

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 $k^{\text{th}}$ 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 potential-representable pure state densities is not dense for $d=3$. Finally, we present an inversion algorithm taking into account degeneracies.

Dates and versions

hal-03099868 , version 1 (06-01-2021)

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Louis Garrigue. Building Kohn-Sham potentials for ground and excited states. 2021. ⟨hal-03099868⟩
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