  We study the classical chaos appearing in a diatomic molecules $BeO$, $CO$
and $CN$ due to the interaction with a circularly polarized electric field, and
its signature in Quantum Mechanics through the Wigner distribution function and
the Boltzmann-Shannon entropy. We found a motion out of the center of the
quantum phase space defined by Wigner function when the classical system
becomes chaotic, and we found a jumping behavior of the average
Boltzmann-Shannon entropy with respect the electric field strength when the
classical system becomes chaotic, indicating a sudden increasing in the
disorder (or sudden lost of information) in the quantum system.
