A new look at Thomas-Fermi Theory

TL;DR

This paper demonstrates that despite its limitations, Thomas-Fermi Theory accurately estimates atomic sizes, supported by numerical, experimental, and mathematical evidence, and proposes new conjectures on its exactness.

Contribution

It provides new evidence for the accuracy of Thomas-Fermi Theory in size estimation and introduces two mathematical conjectures on its potential exactness.

Findings

Thomas-Fermi Theory accurately estimates atomic sizes

Numerical, experimental, and mathematical evidence supports this claim

Proposes two new conjectures on the theory's exactness

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 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.