# On the correlation measure of two-electron systems

## TL;DR

This paper develops an exact analytical model using Hylleraas-type wave functions to quantify electron correlation in two-electron systems, analyzing its impact on charge distributions and information entropies, with implications for understanding atomic correlations.

## Contribution

It introduces a new analytical approach to measure correlation in two-electron systems and examines the effects on charge distributions and Shannon entropies, highlighting the importance of individual entropies.

## Key findings

- Correlation affects charge distributions in two-electron systems.
- The entropy sum approaches a limit for high Z.
- Individual entropies are better measures of correlation.

## Abstract

We make use of a Hylleraas-type wave function to derive an exact analytical model to quantify correlation in two-electron atomic/ionic systems and subsequently employ it to examine the role of inter-electronic repulsion in affecting (i) the bare (uncorrelated) single-particle position- and momentum-space charge distributions and (ii) corresponding Shannon's information entropies. The results presented for the first five members in the helium iso-electronic sequence, on the one hand, correctly demonstrate the effect of correlation on bare charge distributions and, on the other hand, lead us to some important results for the correlated and uncorrelated values of the entropies. These include the limiting behavior of the correlated entropy sum (sum of position- and momentum-space entropies) and geometrical realization for the variation of information entropies as a function of Z. We suggest that, rather than the entropy sum, individual entropies should be regarded as better candidates for the measure of correlation.