Information entropy and complexity measure in generalized Kratzer potential

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.