Potential Surface Properties and Dynamics from Molecular Spectra: A Time-Dependent Picture

  • Eric J. Heller


In this article, a new point of view on the spectroscopic determination of potential surfaces is presented. The perspective is explicitly time dependent, although the theory given here is intended for interpretation of experiments in the frequency domain. We will travel back and forth between the time and frequency domains via Fourier transforms. Some of the characteristics of potential surfaces which we obtain are static ones, such as slopes and directions of excited (in absorption) or ground (in emission) potential surfaces in the Franck-Condon region. Other characterisitics are dynamic ones, involving certain decay and recurrence events which severely limit the form the potential surfaces may take but do not specify it completely.


Periodic Orbit Potential Surface Local Mode Classical Trajectory Transition Moment 
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  1. 1.
    E. J. Heller and W. M. Gelbart, Normal mode spectra in pure local mode molecules, J. Chem. Phys. 73: 626 (1980).CrossRefGoogle Scholar
  2. 2.
    See, e.g., D. F. Smith and J. Overend, Anharmonic force constants of water, Spectrochim. Acta A28: 471 (1972).Google Scholar
  3. 3.
    M. G. Bucknell and N. C. Handy, Vibration-rotation wavefunctions and energies for any molecule obtained by a variational method, Mol. Phys. 28: 771 (1974).Google Scholar
  4. 4.
    E. L. Elert, P. R. Stannard, and W. M. Gelbart, Local mode structure of the water molecule, J. Chem. Phys. 67: 5395 (1978); P. R. Stannard, M. L. Elert, and W. M. Gelbart, On the overtone-combination spectra of BA2 molecules, J. Chem. Phys., to be published.CrossRefGoogle Scholar
  5. 5.
    E. J. Heller, Quantum corrections to classical photodissociation models, J. Chem. Phys. 68: 2066 (1978).CrossRefGoogle Scholar
  6. E. J. Heller, Photofragmentation of triatomic molecules, J. Chem. Phys. 68: 3891 (1978).CrossRefGoogle Scholar
  7. 6.
    K. C. Kulander and E. J. Heller, Time-dependent formulation of polyatomic photofragmentation: Application to H+ 3, J. Chem. Phys. 69: 2439 (1978).CrossRefGoogle Scholar
  8. 7.
    J. A. Beswick and J. Jortner, Absorption lineshapes for the photoabsorption of polyatomic molecules, Chem. Phys. 24: 1 (1977).CrossRefGoogle Scholar
  9. 8.
    R. M, Brown, S.-Y. Lee, D. Tannor, and E. J. Heller, unpublished results.Google Scholar
  10. 9.
    S.-Y. Lee, R. M. Brown, and E. J. Heller, unpublished.Google Scholar
  11. 10.
    E. J. Heller, Phase space interpretation of semiclassical theory, J. Chem. Phys. 67: 3339 (1977).CrossRefGoogle Scholar
  12. 11.
    E. J. Heller, Classical S-matrix limit of wavepacket dynamics, J. Chem, Phys. 65: 4979 (1976). See also reference 6.Google Scholar
  13. 12.
    See, e.g., K. Imre, E. Ozizmir, M. Rosenbaum, and R. F. Zweifel, Wigner method in quantum statistical mechanics, J. Math. Phys. 8: 1097 (1967).CrossRefGoogle Scholar
  14. E. J. Heller, Wigner phase space method: Analysis for semiclassical applications, J. Chem. Phys. 65: 1289 (1976).CrossRefGoogle Scholar
  15. 13.
    E. J. Heller and M. J. Davis, Molecular overtone band widths from classical trajectories, J. Phys. Chem. 84: 1999 (1980).CrossRefGoogle Scholar
  16. 14.
    R. Brown and E. J. Heller, Classical approach to photodissociation: Wigner method, preprint.Google Scholar
  17. 15.
    S.-Y. Lee and E. J. Heller, Time-dependent theory of Raman scattering, J. Chem. Phys. 71: 4777 (1979).CrossRefGoogle Scholar
  18. 16.
    J. M. Schulman, R. Detrano, and J. I. Musher, Inclusion of nuclear motion in calculations of optical properties of diatomic molecules, Phys. Rev. A 5: 1125 (1972).CrossRefGoogle Scholar
  19. J. M. Schulman and R. Detrano, Semiclassical theory of vibrational Raman intensities, Phys. Rev. A 10: 1192 (1974).CrossRefGoogle Scholar
  20. 17.
    G, Placzek, “Handbuch der Radiologie”, Akademie Verlagsgeselleschaft, Leipzig (1934), Vol. 6, Part 2, p. 205; or see English translation: University of California report UCRL 52b(2).Google Scholar
  21. 18.
    I. S. Gradshtezn and I. M. Ryzhik, “Tables of Integrals, Series, and Products”, Academic, New York (1965).Google Scholar
  22. 19.
    G. Eyring, B. Avry, R. Mathies, R. Fransen, I. Palings, and J. Ligtenberg, unpublished.Google Scholar
  23. 20.
    D. W. Turner, C. Baker, A. D. Baker, and C. R. Brundle, “Molecular Photoelectron Spectroscopy”, Wiley, New York (1970).Google Scholar
  24. 21.
    D. D. Smith and A. H. Zewail, Characterization of vibrational overtones and “local” modes by emission spectroscopy, J. Chem. Phys. 71: 540 (1979).CrossRefGoogle Scholar
  25. 22.
    M. J. Davis and E. J. Heller, Quantum dynamical tunneling in bound states, J. Chem. Phys., submitted for publication.Google Scholar
  26. 23.
    D. W. Noid, M. L. Koszykowski, and R. A. Marcus, A spectral analysis method of obtaining molecular spectra from classical trajectories, J. Chem. Phys. 67: 404 (1977).CrossRefGoogle Scholar
  27. 24.
    R. T. Pack, Simple theory of diffuse vibrational structure in continuous UV spectra 1. Collinear photodissociation of tri-atomic molecules, J. Chem. Phys. 65: 4765 (1976).CrossRefGoogle Scholar
  28. 25.
    E. J. Heller, Photofragmentation of symmetric triatomic molecules, J. Chem. Phys. 68: 3891 (1978).CrossRefGoogle Scholar
  29. 26.
    E. J. Heller, E. B. Stechel, and M. J. Davis, Molecular spectra, Fermi resonances, and classical motion, J. Chem. Phys. 73: 4720 (1980).CrossRefGoogle Scholar
  30. 27.
    R. T. Lawton and M. S. Child, Local-mode vibrations of water, Mol. Phys. 37: 1799 (1979).CrossRefGoogle Scholar
  31. R. T. Lawton and M. S. Child, Excited stretching vibrations of water: The quantum mechanical picture, Mol. Phys. 40: 733 (1980).CrossRefGoogle Scholar
  32. 28.
    M. C. Gutzwiller, Periodic orbits and classical quantizations conditions, J. Math. Phys. 12: 343 (1971).CrossRefGoogle Scholar
  33. 29.
    W. H. Miller, Seraiclassical quantization of nonseparable systems: A new look at periodic orbit theory, J. Chem. Phys. 63: 996 (1975).CrossRefGoogle Scholar
  34. 30.
    M. V. Berry and M. Tabor, Closed orbits and the regular bound spectrum, Proc. Roy. Soc. Lond., Ser. A 349: 101 (1976).CrossRefGoogle Scholar
  35. 31.
    H. L. Fang and R. L. Swofford, High excited vibrational states of molecules by thermal lensing spectroscopy and the local-mode model I. CHC13, CHBr3, CH2C12, CH2Br2, J. Chem. Phys. 72: 6382 (1980).CrossRefGoogle Scholar
  36. 32.
    J. S. Fong and C. B. Moore, Bond selective excitation of molecules, in: “S. P. S. Porto Memorial Conference”, Springer-Verlag, Berlin (1980).Google Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Eric J. Heller
    • 1
  1. 1.Department of ChemistryUniversity of CaliforniaLos AngelesUSA

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