Polyad breaking phenomenon associated with a local-to-normal mode transition and suitability to estimate force constants

ABSTRACT

In a system of two interacting harmonic oscillators a local-to-normal mode transition is manifested as a polyad breaking phenomenon. This phenomenon is associated with the suitability to estimate zeroth-order force constants in the framework of a local mode description. This transition is also exhibited in two interacting Morse oscillators. To study this case, an appropriate parameterisation going from a molecule with local mode behaviour (H₂O) to a molecule presenting a normal mode behaviour (CO₂) is introduced. Concepts from quantum mechanics like fidelity, entropy and probability density, as well from nonlinear classical mechanics like Poincaré sections are used to detect the transition region. It is found that fidelity and entropy are sensitive complementary properties to detect the local-to-normal transition. Poincaré sections allow the local-to-normal transition to be detected through the appearance of chaos as a consequence of the polyad breaking phenomenon. In addition, two kinds of avoided energy crossings are identified in accordance with the different regions of the spectrum.

KEYWORDS:

• Interacting oscillators
• local-to-normal mode transition
• force constants
• fidelity
• entropy
• polyad breaking
• Poncaré sections

Acknowledgments

First author is grateful for the scholarship (Posgrado en Ciencias Químicas) provided by CONACyT, México.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by DGAPA-UNAM [project number IN109113], [project number IN227017]; CONACyT [grant number 238494].