Formation of Stable Molecules within the Statistical Theory of Atoms

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Abstract
We show that no theory can describe a stable molecule or molecular ion if it expresses the charge density as a function of the electric potential alone. Such theories comprise the Thomas-Fermi, Thomas-Fermi-Dirac, Thomas-Fermi-Gombás theories. The Thomas-Fermi theory with the Fermi-Amaldi correction cannot give rise to molecular binding for homonuclear, diatomic, neutral molecules if the total number of electrons in the molecule equals or exceeds 4. The Thomas-Fermi-Weizsäcker theory gives stable homonuclear, diatomic molecules.