  In the recent years, information theory of quantum-mechanical systems have
aroused the interest of many Theoretical Physicist. This due to the fact that
it provides a deeper insight into the internal structure of the systems. Also,
It is the strongest support of the modern quantum computation and information,
which is basic for numerous technological developments. This study report the
any $\ell-$state solution of the radial Schr\"{o}dinger equation with the
Mie-type ring shaped diatomic molecular potential. Rotational-vibration of some
few selected diatomic molecules are given. The probability distribution density
of the system which gives the probability density for observing the electron in
the state characterized by the quantum numbers $(n, l, m)$ in the Mie-type ring
shaped diatomic molecular potential is obtained. Finally, we analyze this
distribution via a complementary information measures of a probability
distribution called as the Fisher's information entropy.
