OpenAI research collection · 1 manuscript · Source checked 2026-10-19
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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^∞(\mathbb R^3). This disproves Kohn–Sham ensemble representability for that potential class; the required nuclear charge is specified nonnumerically.
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MANUSCRIPT 01
A Coulomb ground-state density without Kohn-Sham ensemble representation
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^∞(\mathbf R^3). The molecule has two equal positive integer nuclear charges,…
Full source abstract
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^∞(\mathbf R^3). The molecule has two equal positive integer nuclear charges, specified by an exact finite nonnumerical formula.
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New mathematical reasoning could help AI tackle harder scientific and computational problems. How reliably these skills transfer beyond mathematics will determine how much they contribute to general intelligence.