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arXiv · 2610.09997

Asymptotic Neutrality for the Ionization Conjecture in the Two-Center Thomas-Fermi-Dirac-von Weizsäcker Theory

Lu Chen·Yong Wu
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Abstract

The ionization conjecture for the Thomas-Fermi-Dirac-von Weizsäcker model asks how many electrons a given nuclear configuration can bind. So far, only the single-center case has been settled by Frank, Nam, and Van Den Bosch, while the original molecular case has still remained open. We advance this conjecture in the two-center case. We prove that for two distinct nuclei of total charge $Z$, the number $N$ of bound electrons satisfies $N\le Z+C Z^{153/154}(1+\log Z)^{3/8}$, with constants independent of the nuclear positions and the nuclear charges. The proof relies on a comparison with the neutral Thomas-Fermi density and on localization and exterior $L^1$-estimates coupled through the screened potential. Our results could be extended to molecules with any fixed number $K$ of nuclei.

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Lu Chen, Yong Wu. 2026-10-07. Asymptotic Neutrality for the Ionization Conjecture in the Two-Center Thomas-Fermi-Dirac-von Weizsäcker Theory. https://arxiv.org/abs/2610.09997

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