# Upper Estimates for Electronic Density in Heavy Atoms and Molecules

## TL;DR

This paper develops an improved upper estimate for electronic density in heavy atoms and molecules, especially at distances greater than or equal to the inverse of the nuclear charge, surpassing previous bounds.

## Contribution

It introduces a new upper bound for electronic density that is more accurate at certain distances from nuclei in heavy atoms and molecules.

## Key findings

- Upper estimate improves upon known bounds at distances ≥ Z^{-1}
- Estimate is not sharp but still better than previous results
- Applicable to heavy atoms and molecules with large nuclear charge

## Abstract

We derive an upper estimate for electronic density $\rho_\Psi (x)$ in heavy atoms and molecules. While not sharp, on the distances $\gtrsim Z^{-1}$ from the nuclei it is still better than the known estimate $CZ^3$ ($Z$ is the total charge of the nuclei, $Z\asymp N$ the total number of electrons).