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

The correlation diagram of the vibrational energy spectra associated with the stretching modes of triatomic molecules such as CO${}_2$ and H${}_2$O is analyzed by means of two interacting Morse oscillators. By considering a linear dependence 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, it is shown that the fidelity, entropy and Poincar'e sections detect the polyad breaking process manifested in the transition from local to normal mode behaviors. Additionally Poincar'e sections show a transition to chaos where the polyad cannot be defined.