Nonlinear Coupling and Vibrational Dynamics

  • Francois Fillaux
Part of the Progress in Mathematics book series (NSSA)

Abstract

In the previous lecture, we have seen how the molecular vibrations in a quadratic potential can be described in terms of normal modes, i.e., an ensemble of classical harmonic oscillators. The dissociation energy of most of the chemical bonds is much larger than in the lower vibrational states and the corresponding vibrational modes are well described by the harmonic approximation. However, there are some modes which show very large anharmonicity and more sophisticated approaches are. necessary to account for their dynamics. These modes are usually due to oscillations of particles with very large amplitudes (namely CH3 torsional modes, nitrogen inversion, four member ring-puckering, five-member ring pseudo-rotation, etc.) [1]; to chemical bonds with a dissociation energy close to the vibrational energy level (hydrogen bond) [2, 3]; or to weak inter-molecular interactions (Van der Waals, ionic) [4]. Although these vibrational motions are rather rare compared to the total number of vibrational modes in a molecule, a thorough analysis of their dynamics provides an accurate description of the potential functions governing large amplitude displacements of atoms in a molecule or in a complex. These are related to important phenomena in physics and chemistry, such as the transport of atoms or charges, dynamical exchanges between molecular conformations, and the preliminary steps in chemical reactions.

Keywords

Wave Function Proton Transfer Dissociation Energy Vibrational Spectroscopy Morse Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Francois Fillaux
    • 1
  1. 1.Laboratoire de Spectrochimie Infrarouge et RamanCentre National de la Recherche ScientifiqueThiaisFrance

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