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Excited Vibrational States: Semiclassical Self-Consistent-Field and Statistical Considerations

  • Mark A. Ratner
  • R. B. Gerber
  • V. Buch
Chapter
  • 54 Downloads
Part of the NATO ASI Series book series (ASIC, volume 200)

Abstract

An overview is presented of recent studies of highly-excited vibrational states using both self-consistent-field (SCF) and statistical descriptions. The SCF scheme is the simplest possible extension of the separable-modes picture, and provides quite adequate characterization of all vibrational levels at relatively low levels of excitation. At higher energies, above the classical threshold for chaos, most SCF states are too strongly mixed for the description to remain valid. These strongly-mixed situations are best described statistically, and we present some results of statistical studies of molecular energy levels and wavefunctions. Even at high energies, however, some SCF-type states mix only very weakly. These states, for which the SCF-type description remains valid, should show strong spectroscopic features in absorbtion from lower states. They will generally be of “extremal-motion” type, meaning that, because all vibrational energy greater than zero-point energy is concentrated in a single mode (or possibly a very few modes), the amplitudes for intramolecular vibrational energy transfer, and therefore for mixing with other SCF states, are very small. It is suggested that such high-energy SCF states have already been seen spectroscopically in species such as ozone and HCN.

Keywords

Vibrational Energy Vibrational State Configuration Interaction Transition Moment Tunneling Rate 
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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References

  1. 1.
    J.M. Bowman, J. Chem. Phys. 68, 608 (1978).ADSCrossRefGoogle Scholar
  2. 2.
    G.D. Carney, L.I. Sprandel and C.W. Kern, Adv. Chem. Phys. 37, 305 (1978).CrossRefGoogle Scholar
  3. 3.
    M. Cohen, S. Greita and R.P. McEachran, Chem. Phys. Lett. 60, 445 (1979).ADSCrossRefGoogle Scholar
  4. 4.
    J.M. Bowman, K. Christoffel and F. Tobin, J. Phys. Chem. 83, 905 (1979).CrossRefGoogle Scholar
  5. 5.
    H. Romanowski, J.M. Bowman and L.B. Harding, J. Chem. Phys. 82, 4155 (1985).ADSCrossRefGoogle Scholar
  6. 6.
    R.B. Gerber and M.A. Ratner, Chem. Phys. Lett. 68, 195 (1979).ADSCrossRefGoogle Scholar
  7. 7.
    M.A. Ratner, V. Buch and R.B. Gerber, Chem. Phys. 53, 345 (1980).CrossRefGoogle Scholar
  8. 8.
    R.M. Roth, M.A. Ratner and R.B. Gerber, J. Phys. Chem. 87, 2376 (1983).CrossRefGoogle Scholar
  9. 9.
    R.B. Gerber, R.M. Roth and M.A. Ratner, Mol. Phys. 44, 1335 (1981).ADSCrossRefGoogle Scholar
  10. 10.
    R.M. Roth, M.A. Ratner and R.B. Gerber, Phys. Rev. Lett. 52, 1288 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    B. Barboy, G.C. Schatz, M.A. Ratner and R.B. Gerber, Mol. Phys. 50, 353 (1983).ADSCrossRefGoogle Scholar
  12. 12.
    R.B. Gerber and M.A. Ratner, Adv. Chem. Phys., submitted.Google Scholar
  13. 13.
    M.A. Ratner and R.B. Gerber, J. Phys. Chem. 90, 20 (1986).CrossRefGoogle Scholar
  14. 14.
    L.L. Gibson, R.M. Roth, M.A. Ratner and R.B. Gerber, J. Chem. Phys. 85, 3425 (1986).ADSCrossRefGoogle Scholar
  15. 15.
    A.D. Smith, W.-K. Liu and D.W. Noid, Chem. Phys. 89, 345 (1984).CrossRefGoogle Scholar
  16. 16.
    P. Schatzberger, E.A. Halevi and N. Moiseyev, J. Phys. Chem. 89, 4691 (1985).CrossRefGoogle Scholar
  17. 17.
    T.C. Thompson and D.G. Truhlar, J. Chem. Phys. 77, 3031 (1982).ADSCrossRefGoogle Scholar
  18. 18.
    C. E. Porter, Statistical Theories of Spectra: Fluctuations ( Academic, New York, 1965 ).Google Scholar
  19. 19.
    T.A. Brody et. al., Revs. Mod. Phys. 53, 385 (1981).MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    W.P. Halperin, Revs. Mod. Phys. 58, 533 (1986).ADSCrossRefGoogle Scholar
  21. 21.
    V. Buch, R.B. Gerber and M.A. Ratner, J. Chem. Phys. 76, 5397 (1982).ADSCrossRefGoogle Scholar
  22. 22.
    V. Buch, M.A. Ratner and R.B. Gerber, Mol. Phys. 46, 1129 (1982).ADSCrossRefGoogle Scholar
  23. 23.
    R.B. Gerber, V. Buch and M.A. Ratner, Chem. Phys. Lett. 89, 171 (1982).ADSCrossRefGoogle Scholar
  24. 24.
    P. Pechukas, Phys. Rev. Lett. 51, 943 (1983).MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    E.B. Stechel and E.J. Heller, Ann. Revs. Phys. Chem. 35, 563 (1985).ADSCrossRefGoogle Scholar
  26. 26.
    E. Haller, H. Köppel and L.S. Cederbaum, Phys. Rev. Lett. 52, 1665 (1984).ADSCrossRefGoogle Scholar
  27. 27.
    H. Romanowski, M.A. Ratner and R.B. Gerber, unpublished.Google Scholar
  28. 28.
    A. Chedin, J. Mol. Spectros 76, 430 (1979).ADSCrossRefGoogle Scholar
  29. 29.
    e.g. M.S. Child and L. Halonen, Adv. Chem. Phys. 57, 1 (1984).CrossRefGoogle Scholar
  30. 30.
    B.R. Henry, Acc. Chem. Res. 10, 207 (1977).CrossRefGoogle Scholar
  31. 31.
    R. Lefebvre, Int. J. Quant. Chem. 23, 543 (1983).CrossRefGoogle Scholar
  32. 32.
    N. Moiseyev, Chem. Phys. Lett. 98, 223 (1983).Google Scholar
  33. 33.
    K.K. Lehmann, G. Scherer and W.A. Klemperer, J. Chem. Phys. 77, 2853 (1982); G.J. Scherer, K.K. Lehmann and W.A. Klemperer, J. Chem. Phys. 78, 2817 (1983).ADSCrossRefGoogle Scholar
  34. 34.
    D.E. Reisner, P.H. Vaccaro, C. Kittrell, R.W. Field, J.L. Kinsey and H-L Dai, J. Chem. Phys. 77, 575 (1982); D.E. Reisner, R.W. Field, J.L. Kinsey and H-L Dai, J. Chem. Phys. 78, 2817 (1983); E. Abramson, R.W. Field, D Imre, K.K. Innes and J.L. Kinsey, J. Chem. Phys. 83, 453 (1985).ADSCrossRefGoogle Scholar
  35. 35.
    D. Bailly, R. Farrenq, G. Guelachivili and C. Rossetti, J. Mol. Spectros. 90, 74 (1981).ADSCrossRefGoogle Scholar
  36. 36.
    Z. Bacic, R.B. Gerber and M.A. Ratner, J. Phys. Chem. 90, 3606 (1986).CrossRefGoogle Scholar
  37. 37.
    D.H. Farrelly and A.D. Smith, J. Phys. Chem. 90, 1599 (1986).CrossRefGoogle Scholar
  38. 38.
    R.B Gerber, V. Buch, M.A. Ratner, J. Chem. Phys. 77, 3022 (1982).ADSCrossRefGoogle Scholar
  39. 39.
    G.C. Schatz, V. Buch, M.A. Ratner and R.B Gerber, J. Chem. Phys. 79, 1808 (1983).ADSCrossRefGoogle Scholar
  40. 40.
    V. Buch, R.B. Gerber, and M.A. Ratner, J. Chem. Phys. Lett. 101, 44 (1983).ADSCrossRefGoogle Scholar
  41. 41.
    Z. Kirson, R.B. Gerber, A. Nitzan, and M.A. Ratner, Surface Sci. 137, 527 (1984).ADSCrossRefGoogle Scholar
  42. 42.
    L.A. Eslava, R.B. Gerber and M.A. Ratner, Mol. Phys. 56, 47 (1985).ADSCrossRefGoogle Scholar
  43. 43.
    R.B Gerber, Z. Bacic and M.A. Ratner, Mol. Phys. 56, 47 (1985).ADSCrossRefGoogle Scholar
  44. 44.
    e.g. R.L. Sundberg, E. Abramson, J.L. Kinsey and R.W. Field, J. Chem. Phys. 83, 466 (1985); S. Mukamel, J. Sue and A. Pandey, Chem. Phys. Lett. 105, 134 (1984).ADSCrossRefGoogle Scholar
  45. 45.
    V. Buch, R.B. Gerber and M.A. Ratner, J. Chem. Phys. 81, 3393 (1984).ADSCrossRefGoogle Scholar
  46. 46.
    L. Gibson, unpublished.Google Scholar
  47. 47.
    V. Buch, unpublished.Google Scholar
  48. 48.
    H. Romanowski, M.A. Ratner, R.B. Gerber, to be published.Google Scholar
  49. 49.
    K. Stefanski and H.S. Taylor, Phys. Rev. A. 31, 2810 (1985); H.S. Taylor, preprint.MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    D. Imre, Ph.D. Thesis, Mass Inst. of Technology, 1985.Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Mark A. Ratner
    • 1
  • R. B. Gerber
    • 2
  • V. Buch
    • 3
  1. 1.Department of ChemistryNorthwestern UniversityEvanstonUSA
  2. 2.Fritz Haber Center for Molecular Dynamics and Department of Physical ChemistryHebrew UniversityJerusalemIsrael
  3. 3.Harvard College ObservatoryCambridgeUSA

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