# Information entropy and complexity measure in generalized Kratzer potential

## TL;DR

This paper analyzes Shannon entropy, Fisher information, and complexity measures for diatomic molecules under the generalized Kratzer potential, deriving exact expressions and exploring how these measures change with molecular state and ionization.

## Contribution

It provides exact analytical expressions for Fisher information in diatomic molecules and investigates the behavior of entropy and complexity measures across different molecular states.

## Key findings

- Fisher information increases from neutral to cationic molecules.
- Shannon entropy decreases with ionization.
- Complexity measure increases with the number of nodes.

## Abstract

Shannon entropy ($S$), Fisher information ($I$) and a measure equivalent to Fisher-Shannon complexity $(C_{IS})$ of a ro-vibrational state of diatomic molecules (O$_2$, O$_2^+$, NO, NO$^+$) with generalized Kratzer potential is analyzed. \emph{Exact} analytical expression of $I_{\rvec}$ is derived for the arbitrary state, whereas the same could be done for $I_{\pvec}$ with $\{n,\ell,m=0\}$ state. It is found that shifting from neutral to the cationic system, $I_{\rvec}$ increases while $S_{\rvec}$ decreases, consistent with the interpretation of a localization in the probability distribution. Additionally, this study reveals that $C_{IS}$ increases with the number of nodes in a system.