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The correlation diagram of the vibrational energy spectra associated with thestretching modes of triatomic molecules such as CO$_2$ and H$_2$O is analyzedby means of two interacting Morse oscillators. By considering a lineardependence of the structure and force constants ($x_g=g^o_{rr'}/g^o_{rr},x_f=f_{rr'}/f_{rr}$) going from the water parameters to the carbon dioxide, itis shown that the fidelity, entropy and Poincar\'e sections detect the polyadbreaking process manifested in the transition from local to normal modebehaviors. Additionally Poincar\'e sections show a transition to chaos wherethe polyad cannot be defined.

Fidelity, entropy, and Poincar\'e sections as tools to study the polyad breaking phenomena