  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.
