A new look at Thomas–Fermi theory

ABSTRACT

In this short note, we argue that Thomas–Fermi theory, the simplest of all density functional theories, although failing to explain features such as molecular binding or stability of negative ions, is surprisingly accurate in estimating sizes of atoms. We give both numerical, experimental and rigorous mathematical evidence for this claim. Motivated by this, we formulate two new mathematical conjectures on the exactness of Thomas–Fermi theory.

GRAPHICAL ABSTRACT

Keywords:

• Thomas–Fermi theory
• atomic radii
• Born–Oppenheimer curves
• Hartree–Fock theory
• ionisation conjecture

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. I would like to thank Andreas Savin for pointing out that there could be an interest in generalizing the result beyond Hartree-Fock Theory

Additional information

Funding

This work was supported by the European Research Council under ERC Advanced Grant [grant number 321029].