Ground state energy is not always convex in the number of electrons

We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has been conjectured for decades and plays an important role in quantum chemistry. Our counterexample invo...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Simone Di Marino, Lewin, Mathieu, Nenna, Luca
Format: Article
Language:English
Subjects:
Convexity
Coulomb potential
Electrons
Ground state
Nuclei (nuclear physics)
Quantum chemistry
Online Access:Get full text
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Summary:We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has been conjectured for decades and plays an important role in quantum chemistry. Our counterexample involves six nuclei with small fractional charges placed far apart. The ground state energy of 3 electrons is shown to be higher than the average of the energies for 2 and 4 electrons. We also show that the nuclei can bind 2 or 4 electrons, but not 3. This article raises the question of whether the energy convexity really holds for all possible molecules (with nuclei of integer charge).
ISSN:2331-8422
DOI:10.48550/arxiv.2409.08632