Shannon entropies and Fisher information of K-shell electrons of neutral atoms

TL;DR

This paper investigates how electronic correlation affects Shannon entropies and Fisher information of K-shell electrons in neutral atoms, using Hylleraas-type wave functions to analyze changes in charge densities.

Contribution

It introduces a simple method to derive charge densities and examines the impact of electron correlation on information measures for K-shell electrons.

Findings

Correlation increases position-space Shannon entropy.

Correlation decreases momentum-space Shannon entropy.

Fisher information shows opposite behavior to Shannon entropy with correlation.

Abstract

We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron-electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position- and momentum-space charge densities, $\rho(\vec{r})$ and $\gamma(\vec{p})$ respectively. We make use of the results for $\rho(\vec{r})$ and $\gamma(\vec{p})$ to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies ($S$) and of Fisher information ($F$) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of $S$ and $F$ to electronic correlation.