# Dihedral Molecular Configurations Interacting by Lennard-Jones and Coulomb Forces

## TL;DR

This paper studies the periodic vibrations of particles arranged in dihedral configurations influenced by Lennard-Jones and Coulomb forces, classifying solutions with symmetries and identifying critical frequencies for small oscillations.

## Contribution

It introduces a topological classification of symmetric periodic solutions using the gradient equivariant degree and provides formulas for the spectrum of the linearized system.

## Key findings

- Classification of periodic solutions with symmetries
- Formulas for the spectrum of the linearized system
- Identification of critical frequencies for particle motions

## Abstract

In this paper, we investigate periodic vibrations of a group of particles with a dihedral configuration in the plane governed by the Lennard-Jones and Coulomb forces. Using the gradient equivariant degree, we provide a full topological classification of the periodic solutions with both temporal and spatial symmetries. In the process, we provide with general formulae for the spectrum of the linearized system which allows us to obtain the critical frequencies of the particle motions which indicate the set of all critical periods of small amplitude periodic solutions emerging from a given stationary symmetric orbit of solutions.