Failure of Kohn–Sham ensemble representation

1 paper

Constructs a three-electron Coulomb molecule with two equal positive-integer-charge nuclei whose absolute ground-state density has no noninteracting ground-state ensemble representation by a single real spin-independent local potential in \(L^{3/2}(\mathbb R^3)+L^\infty(\mathbb R^3)\). This disproves Kohn–Sham ensemble representability for that potential class; the required nuclear charge is specified nonnumerically.

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Papers 1

A Coulomb ground-state density without Kohn-Sham ensemble representation

OpenAI · September 25, 2026

We construct a finite three-electron Coulomb molecule whose spin-summed ground-state density cannot be reproduced by any ground-state ensemble of noninteracting electrons in a single real, spin-independent local potential in \(L^{3/2}(\mathbf R^3)+L^\infty(\mathbf R^3)\). The molecule has two equal positive integer nuclear charges, specified by an exact finite nonnumerical formula.

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@misc{OAI:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026,
  author = {{OpenAI}},
  title = {{A Coulomb ground-state density without Kohn--Sham ensemble representation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf}{OAI:A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026}},
  year = {2026}
}

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