Dihedral Molecular Configurations Interacting by Lennard-Jones and\n Coulomb Forces

2017/02/14 by Irina Berezovik, Berezovik, Irina, Qingwen Hu +3 · 3 citations
Physics and Astronomy · Chemistry · #Quantum chaos and dynamical systems #Molecular Spectroscopy and Structure #Astrophysics and Star Formation Studies

paper · pdf · doi:10.48550/arxiv.1702.04234

Abstract

In this paper, we investigate periodic vibrations of a group of particles\nwith a dihedral configuration in the plane governed by the Lennard-Jones and\nCoulomb forces. Using the gradient equivariant degree, we provide a full\ntopological classification of the periodic solutions with both temporal and\nspatial symmetries. In the process, we provide with general formulae for the\nspectrum of the linearized system which allows us to obtain the critical\nfrequencies of the particle motions which indicate the set of all critical\nperiods of small amplitude periodic solutions emerging from a given stationary\nsymmetric orbit of solutions.\n

Cited by

• Nonlinear Dynamics In Optimization Landscape of Shallow Neural Networks with Tunable Leaky ReLU
• Nonlinear Vibrational Mode of Molecule with Octahedral Configuration
• Global Bifurcation In Four-Component Bose-Einstein Condensates In Space

Related

• Symmetries of Nonlinear Vibrations in Tetrahedral Molecular\n Configurations
• Molecular chains interacting by Lennard-Jones and Coulomb forces
• Symmetric Molecular Dynamics
• Nonlinear Vibrational Mode of Molecule with Octahedral Configuration
• Properties of large-amplitudes vibrations in dynamical systems with discrete symmetry. Geometrical aspects