Symmetries of Nonlinear Vibrations in Tetrahedral Molecular Configurations

TL;DR

This paper classifies the symmetries of nonlinear vibrational modes in tetrahedral molecular configurations, using topological methods to analyze periodic solutions with various force fields.

Contribution

It provides a comprehensive topological classification of vibrational symmetries in tetrahedral molecules, applicable to general force interactions.

Findings

Complete symmetry classification of nonlinear vibrations

Application of equivariant gradient degree method

Framework applicable to various force fields

Abstract

We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretching and van der Waals forces. Using equivariant gradient degree, we present a full topological classification of the spatio-temporal symmetries of the periodic solutions. This procedure gives all the symmetries of the nonlinear vibrations for general force fields.