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Failure of Kohn–Sham ensemble representation

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

Sep 25, 2026·paper.pdf

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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