Upper bounds of local electronic densities in molecules

TL;DR

This paper establishes a theoretical upper limit on local electronic densities in molecules, highlighting how electron repulsion prevents excessive electron concentration, based on properties of eigenfunctions of electronic Hamiltonians.

Contribution

It provides a novel a priori upper bound for local electron densities in molecules, connecting electron repulsion and eigenfunction antisymmetry.

Findings

Upper bounds restrict local electron densities in molecules.

Electron repulsion prevents high local electron concentration.

Relation between one- and two-electron densities is key to the proof.

Abstract

The eigenfunctions of electronic Hamiltonians determine the stable structures and dynamics of molecules through the local distributions of their densities. In this paper an a priori upper bound for such local distributions of the densities is given. The bound means that concentration of electrons is prohibited due to the repulsion between the electrons. A relation between one-electron and two-electron densities resulting from the antisymmetry of the eigenfunctions plays a crucial role in the proof.