The Complex Energy Spectrum of Isomeric Reactions

TL;DR

This paper analyzes the energy spectrum of isomeric reactions, showing how the transition between oscillatory and rotational modes leads to chaos, modeled by the Mathieu-Hill equation.

Contribution

It demonstrates that the chaotic energy spectrum in isomerization corresponds to the merging of oscillatory and rotational motion modes, modeled through the Mathieu-Hill equation.

Findings

Chaotic energy regions occur where motion modes merge.

Mathieu-Hill equation describes both oscillatory and rotational modes.

Chaotic behavior linked to mode transition in isomerization.

Abstract

The internal motion in a molecule, in which isomerization processes occur, is characterized by two essentially different modes of motion - oscillatory and rotational. The quantum equation of motion which describes an isomerization process is reduced to the Mathieu-Hill equation. As is known, this equation is able to describe both modes. In the paper, it is shown that the chaotic region of the energy spectrum characterizing an isomerization process corresponds to the region where two modes of motion are merged together.