Using correlation diagrams to study the vibrational spectrum of highly nonlinear floppy molecules: The K-CN case

TL;DR

This paper uses correlation diagrams with variable Planck constant to explore the vibrational spectrum of the nonlinear K-CN molecule, revealing classical structures and a quantum transition from order to chaos.

Contribution

It introduces a novel approach of varying the Planck constant in correlation diagrams to uncover classical structures and chaos in the vibrational states of a nonlinear molecule.

Findings

Classical KAM tori appear as diabatic states in quantum correlation diagrams.

A quantum transition from order to chaos is identified.

Correlation diagrams reveal hidden structures not seen at fixed Planck constant.

Abstract

The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum manifestations of chaos in such dynamical systems. In this paper, we consider the highly nonlinear K-CN molecule, showing how the regular classical structures, i.e., Kolmogorov-Arnold-Moser tori, existing in the mixed classical phase space appear in the quantum levels correlation diagram as emerging diabatic states, something that remains hidden when only the actual value of the Planck constant is considered. Additionally, a quantum transition from order to chaos is unveiled with the aid of these correlation diagrams, where it appears as a frontier of scarred functions.