Nonlinear Coupling and Vibrational Dynamics

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


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.


Wave Function Proton Transfer Dissociation Energy Vibrational Spectroscopy Morse Potential 
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  1. 1.
    J.R. Durig, cd., “Vibrational Spectra and Structure,” vol. 1, Marcel Dekker Inc., New York (1972).Google Scholar
  2. 2.
    G. Zundel and C. Sandorfy, eds., “The Hydrogen Bond. Recent Developments in Theory and Experiments,” vols. 1–3, P. Schuster, North-Holland, Amsterdam (1976).Google Scholar
  3. 3.
    A. Novak, Struct.Bondine 18: 177 (1974).Google Scholar
  4. 4.
    H. Ratajczak and W.J. Orville-Thomas, in “Molecular Interactions,” vol. 1, Wiley and Sons, New York (1980).Google Scholar
  5. 5.
    G. Herzberg, “Infrared and Raman Spectra of Polyatomic Molecules,” Van Nostrand, New York (1960).Google Scholar
  6. 6.
    L. Landau and E. Lifchitz, “Mécanique Quantique,” Mir, Moscow (1967).Google Scholar
  7. 7.
    E. Heilbroner, H. Rutishauser and F. Gcrson, Hclv.Chim.Acta 42: 2285 (1959).CrossRefGoogle Scholar
  8. 8.
    E. Heilbroncr, H. Rutishauser and F. Gerson, Hclv.Chim.Acta 42: 230 (1959).Google Scholar
  9. 9.
    R.L. Somorjai and D.F. Hornig, J.Chem.Phvs. 36: 1980 (1962).Google Scholar
  10. 10.
    S.I. Chan and D. Stelman, J.Chem.Phys. 39: 545 (1963).Google Scholar
  11. 11.
    Y. Guissani and H. Ratajczak, Chem.Phys. 19: 361 (1981).Google Scholar
  12. 12.
    F. Filiaux, M.H. Baron, C. de Loin and G. Salon, J.Raman Spectr. 7: 244 (1978).CrossRefGoogle Scholar
  13. 13.
    F. Fillaux and M.H. Baron, Chem.Phys. 62: 275 (1981).CrossRefGoogle Scholar
  14. 14.
    L. Pauling, “The Nature of the Chemical Bond”, Cornell, Ithaca (1960).Google Scholar
  15. 15.
    G.N. Ramachandran, A.V. Lakshminarayanan and A.S. Kolaskar, 303: 8 (1973).Google Scholar
  16. 16.
    J.O. Thomas, R. Tellegren and I. Olovsson, Acta Cryst. B30: 1155 (1974).CrossRefGoogle Scholar
  17. 17.
    J.O. Thomas, R. Tellegren and I. Olovsson, Acta Cryst. B30: 254 (1974).Google Scholar
  18. 18.
    F. Filiaux, Chem.Phys. 74: 405 (1983).CrossRefGoogle Scholar
  19. 19.
    F. Filiaux, J. Tomkinson and J. Penfold, Chem.Phys. (in press).Google Scholar
  20. 20.
    A. Witkowski and Y. Maréchal, J.Chem.Phys. 48: 3697 (1968).Google Scholar
  21. 21.
    C.A. Coulson and G. N. Robertson, Proc.Rov.Soc. A337: 167 (1974).Google Scholar
  22. 22.
    C.A. Coulson and G. N. Robertson, Proc.Rov.Soc. A342: 289 (1975).CrossRefGoogle Scholar
  23. 23.
    Y. Bouteiller and E. Maréchal, Mol.Phys. 32: 277 (1976).CrossRefGoogle Scholar
  24. 24.
    Y. Bouteiller and Y. Guissani, Mol.Phys. 38: 617 (1979).CrossRefGoogle Scholar
  25. 25.
    J.C. Lassègues and J. Lascombe, in: “Vibrational Spectra and Structure,” p. 51, J.R. Durig, cd., Elsevier (1982).Google Scholar
  26. 26.
    B.I. Stepanov, Zh.Fiz.Khim. 19:507 (1945); and 20: 408 (1946).Google Scholar
  27. 27.
    B.I. Stepanov, Nature London, 157: 808 (1946).CrossRefGoogle Scholar
  28. 28.
    S.A. Barton and W.R. Thorson, J.Chem.Phvs. 71: 4263 (1969).CrossRefGoogle Scholar
  29. 29.
    F. Filiaux, Chem.Phys. 62: 287 (1981).CrossRefGoogle Scholar
  30. 30.
    F. Filiaux, unpublished results.Google Scholar
  31. 31.
    A.S. Davydov, Stud.Biophysics 62: 1 (1977).Google Scholar
  32. 32.
    A.S. Davydov, Phys.Scr. 20: 387 (1979).CrossRefGoogle Scholar
  33. 33.
    A.S. Davydov, Phys.Stat.Sol.(b) 138: 559 (1986).CrossRefGoogle Scholar
  34. 34.
    F. Filiaux, Chem.Phys. 74: 395 (1983).CrossRefGoogle Scholar
  35. 35.
    F. Filiaux, B. Marchon and A. Novak, Chem.Phys. 86: 127 (1984).CrossRefGoogle Scholar
  36. 36.
    L. Soulard and F. Filiaux, Chem.Phys. 100: 355 (1985).Google Scholar
  37. 37.
    P. Bernardet and F. Filiaux, Chem.Phys. 106: 447 (1986).CrossRefGoogle Scholar
  38. 38.
    F. Filiaux, A. Lautié and J. Tomkinson, unpublished results.Google Scholar

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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