Bound on the Excess Charge of Generalized Thomas-Fermi-Weizs\"acker Functionals

TL;DR

This paper establishes bounds on the maximum excess electrons an atom can bind using generalized density functionals, proving the excess charge conjecture for certain powers and analyzing critical behavior at specific parameters.

Contribution

It proves the excess charge conjecture for a range of powers in generalized Thomas-Fermi-Weizs"acker functionals and analyzes the critical case at p=3/2.

Findings

For 3/2<p<2, the excess charge is uniformly bounded in atomic number Z.

At p=3/2, the bound shifts from uniform to linear at a critical coupling.

The linear bound is improved for all p≥6/5.

Abstract

We bound the number of electrons $Q$ that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizs\"acker functional: instead of the classical power $5/3$ more general powers $p$ are considered. For $3/2<p<2$ we prove the excess charge conjecture, i.e., that $Q$ is uniformly bounded in the atomic number $Z$. The case $p=3/2$ is critical: the behavior changes from a uniform bound in $Z$ to a linear bound at the critical coupling $4\sqrt\pi$ of the nonlinear term. We also improve the linear bound for all $p\geq6/5$.