Advertisement

Rotational Spectral Band Shapes in Dense Fluids

  • W. A. Steele

Abstract

Although the detailed structure of infrared or Raman vibration-rotation spectra for low pressure gases is ordinarily interpreted in terms of energy levels, one can also view measurements of the rotational transitions as a method of determining quantized values of the angular momentum of an isolated molecule. In this way, one sees that spectral experiments probe the time evolution of molecular orientations even at low density. As the density increases, the rotational lines broaden and eventually merge into a continuous spectral band. At this point, it is no longer useful to describe the molecules as being in well-defined energy or angular momentum states. A more rewarding approach to the understanding of these band shapes can be found by extracting time-correlation functions from the data by Fourier transforming the band shapes. In general, a time-correlation function contains information about the evolution of some relevant molecular variable averaged over an equilibrium ensemble of molecules; for rotational spectra, the relevant variables are functions of orientation angles It should be emphasized that a Fourier transform of a spectral intensity distribution does not carry one very far toward solving the problem, which is to extract information about vibrational and rotational motions of molecules in dense phases from the data. It is only when one actually begins to model, either by a physical theory or by computer simulation, that the power of the time-correlation function approach becomes apparent.

Keywords

Correlation Function Memory Function Dense Fluid Free Rotation Band Shape 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    R.G. Gordon, Adv.Mag.Res., 3, 1 (1968)Google Scholar
  2. (2).
    R.T. Bailey, in Spec.Per.Reports, Molecular Spectroscopy, Vol. 2, Chemical Soc., London (1972)Google Scholar
  3. (3).
    W.A. Steele, Adv.Chem.Phys., 34, 1 (1976)CrossRefGoogle Scholar
  4. (4).
    D. Oxtoby, this volumeGoogle Scholar
  5. (5).
    G. Birnbaum, this volumeGoogle Scholar
  6. (6).
    R. Kubo, in “Lectures in Theoretical Physics”, Vol.I, Ed. W.E. Britten and L.G. Dunham, Interscience (1959) p. 151Google Scholar
  7. (7).
    J.T. Hynes, Ph.D. Thesis, Princeton University (1965)Google Scholar
  8. (8).
    D.A. Long, “Raman Spectroscopy”, McGraw-Hill (1977) Chap.3Google Scholar
  9. (9).
    C. Brot, in Spec.Per.Reports, Dielectric and Related Molecular Processes, Vol.2 (1973) p. 1; S. Adelman and J.M. Deutch, Adv.Chem.Phys., 31 (1975)Google Scholar
  10. (10).
    See, for example, B.M. Ladanyi and T. Keyes, Molec.Phys., 33, 1067, 1247 (1977); T. Keyes and B.M. Ladanyi, Molec.Phys., 33, 1099, 1271 (1977)Google Scholar
  11. (11).
    P. Mirone and G. Fini, J.Chem.Phys., 71, 2241 (1979) and references contained thereinCrossRefGoogle Scholar
  12. (12).
    B.J. Berne and R.J. Pecora, “Dynamic Light Scattering”, Wiley (1976)Google Scholar
  13. (13).
    L.A. Nafie and W.L. Peticolas, J.Chem.Phys., 57, 3145 (1972).See also F.J. Bartoli and T.A. Litovitz, J.Chem.Phys., 56, 404, 413 (1972)CrossRefGoogle Scholar
  14. (14).
    M.E. Rose, “Elementary Theory of Angular Momentum”, Wiley (1957)Google Scholar
  15. (15).
    W.A. Steele, Molec.Phys., in pressGoogle Scholar
  16. (16).
    P.D. Maker, Phys.Rev., A 1, 923 (1970)CrossRefGoogle Scholar
  17. (17).
    J. Bjarnason, B.S. Hudson and H.C. Andersen, J.Chem.Phys., 70, 4130 (1979)CrossRefGoogle Scholar
  18. (18).
    H.H. Nielsen, Rev.Mod.Phys., 23, 90 (1951)CrossRefGoogle Scholar
  19. (19).
    J.H. Meal and S.R. Polo, J.Chem.Phys., 24, 1119 (1956)CrossRefGoogle Scholar
  20. (20).
    R.M. Lynden-Bell, Molec.Phys., 31, 1653 (1976)CrossRefGoogle Scholar
  21. (21).
    K. Müller and F. Kneubühl, Chem.Phys., 8, 468 (1975)CrossRefGoogle Scholar
  22. (22).
    M. Gilbert, P. Nectoux and M. Drifford, J.Chem.Phys., 68, 679 (1978)CrossRefGoogle Scholar
  23. (23).
    K.T. Gillen and J.E. Griffiths, Chem.Phys., Letters, 17, 359 (1972)CrossRefGoogle Scholar
  24. (24).
    R.G. Gordon, J.Chem.Phys., 38, 2788 (1963); 40, 1973 (1964); 41, 1819 (1964)CrossRefGoogle Scholar
  25. (25).
    B.J. Berne and G.D. Harp, Adv.Chem.Phys., 17, 63 (1970)CrossRefGoogle Scholar
  26. (26).
    M.W. Evans, Spec.Per.Reports, “Dielectric and Related Molecular Processes”, Vol. 3 (1977) p. 1Google Scholar
  27. (27).
    W.A. Steele and W.B. Street, Molec.Phys., in pressGoogle Scholar
  28. (28).
    A.A. Maryott, M.S. Malmberg and K.T. Gillen, Chem.Phys., Letters, 25, 169 (1974)CrossRefGoogle Scholar
  29. (29).
    G. Levi and M. Chalaye, Chem.Phys., Letters, 19, 263 (1973); J.P. Marsault, F. Marsault-Herail and G. Levi, Molec.Phys., 33, 735 (1977); J. Vincent-Geisse, J. Soussen-Jacob, T. Nguyen Tan and R.E.D. McClung, Can.J.Phys., 57, 564 (1979)CrossRefGoogle Scholar
  30. (30).
    R.G. Gordon, J.Chem.Phys., 44, 1830 (1966)CrossRefGoogle Scholar
  31. (31).
    F. Bliot, C. Abbar and E. Constant, Molec. Phys., 24, 241 (1972); F. Bliot and E. Constant, Chem.Phys., Letters, 253 (1973); 29, 618 (1974)CrossRefGoogle Scholar
  32. (32).
    K. Singer, J.V.L. Singer and A. J. Taylor, Molec.Phys., 37, 1239 (1979)CrossRefGoogle Scholar
  33. (33).
    B. Quentrec and C. Brot, Phys.Rev., A 12, 272 (1975)Google Scholar
  34. (34).
    G.H. Wegdam, G.J. Evans and M. Evans, Adv.Molec.Relax, and Interaction Processes, 11 295 (1977)CrossRefGoogle Scholar
  35. (35).
    D. Kivelson and P. Madden, Molec.Phys., 30, 1749 (1975); T. Keyes and D. Kivelson, J.Chem.Phys., 56, 1057 (1972); B. Guillot and S. Bratos, Molec.Phys., 37, 991 (1979)CrossRefGoogle Scholar
  36. (36).
    J. O’Dell and B.J. Berne, J.Chem.Phys., 63, 2376 (1975)CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • W. A. Steele
    • 1
  1. 1.Department of Chemistry 152 Davey LaboratoryThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations