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

TL;DR

This paper investigates how fidelity, entropy, and Poincaré sections can be used to analyze polyad breaking in vibrational spectra of triatomic molecules, revealing transitions from local to normal modes and the onset of chaos.

Contribution

It introduces a combined use of fidelity, entropy, and Poincaré sections to detect polyad breaking and chaos in molecular vibrational spectra.

Findings

Fidelity and entropy detect the transition from local to normal mode behavior.

Poincaré sections reveal the transition to chaotic dynamics.

Polyad cannot be defined once chaos sets in.

Abstract

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.