Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acker theory with small nuclear charges

TL;DR

This paper investigates the ionization problem within the Thomas-Fermi-Dirac-von Weizs"acker model, demonstrating the nonexistence of energy minimizers for atoms and molecules under certain conditions, especially with small nuclear charges.

Contribution

It proves the nonexistence of minimizers in the model for large electron numbers and small nuclear charges, extending to cases with decaying external potentials and arbitrary nuclear charges.

Findings

No minimizers for large electron counts with small nuclear charges.

Nonexistence of stable and radial minimizers for arbitrary nuclear charges.

Results apply to external potentials decaying faster than Coulomb potential.

Abstract

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizs\"acker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.