Nonlinear Vibrational Mode of Molecule with Octahedral Configuration

TL;DR

This paper analyzes the nonlinear vibrational modes of octahedral molecules, specifically SF6, using equivariant degree theory to prove the existence of multiple symmetric periodic solutions and illustrating these modes numerically.

Contribution

It introduces a mathematical approach to identify and prove the existence of multiple vibrational modes in octahedral molecules, expanding understanding of their nonlinear dynamics.

Findings

Existence of at least 16 symmetric vibrational modes.

Application of equivariant gradient degree to molecular vibrations.

Numerical animations illustrating vibrational modes.

Abstract

In this work, we investigate the nonlinear dynamics of molecules with an octahedral configuration, with particular focus on sulfur hexafluoride SF6. Under the assumption of isotypic nonresonance, we apply the method of equivariant gradient degree to prove the existence of branches of periodic solutions emerging from the critical orbit of equilibrium, corresponding to at least 16 distinct types of symmetries with maximal orbit kinds. Numerical animations are presented to illustrate the detected vibrational modes.