Advertisement

Applied physics

, Volume 15, Issue 2, pp 213–218 | Cite as

The identification of nonlinear molecular systems by spectroscopic methods

  • T. W. Barrett
Contributed Papers

Abstract

The Wiener functional expansion method for the analysis of nonlinear systems is applied to identify and analyze both nonlinear and linear molecular systems by spectroscopic methods. As the sampling filter (monochromator) of any spectroscopic apparatus may be defined by a Weber-Hermite polynomial, an analysis of the refracted or scattered light by orthogonal polynomials is easily achieved. Time averaging obtains the Weber-Hermite coefficients which permit the characterization of the molecular system with respect to the polarization of the incident and scattered light. In the case of two series of measurements made with incident and emerging light polarized in different directions: the identification of the JonesM matrices for the molecular system irradiated is possible. In the case of three series of measurements made, for example, with incident and emerging light (a) circularly polarized corotating, (b) circularly polarized contrarotating, and (c) plane polarized perpendicular: the identification of the molecular system's McClain invariants related to the vibrational symmetry group for Raman inelastic light scattering is possible. The analysis presents a unified picture of elastic and inelastic light scattering and one-photon and two-photon processes. The apparatus described would detect those instances in molecular systems for which Beer's law does not apply.

PACS

42.65 42.80 32 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N.Wiener:Nonlinear Problems in Random Theory (M.I.T. Press, Cambridge, MA 1958)MATHGoogle Scholar
  2. 2.
    Y.W.Lee:Selected Papers of Norbert Wiener (M.I.T. Press, Cambridge, MA 1964) pp. 17–33Google Scholar
  3. 3.
    G.H.Harris, L.Lapidus: Industr. & Eng. Chem.59, 66–81 (1967)CrossRefGoogle Scholar
  4. 4.
    G.Szego:Orthogonal Polynomials. Am. Math. Soc. Coll. Publ. V.23 (Am. Math. Soc., Providence, Rhode Island, 4th edition, 1975)Google Scholar
  5. 5.
    T.W.Barrett: J. Sound & Vibr.39, 265–268 (1975)Google Scholar
  6. 6.
    T.W.Barrett: J. Sound & Vibr.41, 259–261 (1975)CrossRefGoogle Scholar
  7. 7.
    T.W.Barrett: Acustica33, 149–165 (1975)Google Scholar
  8. 8.
    T.W.Barrett: Acustica36, 271–281 (1976)ADSGoogle Scholar
  9. 9.
    R.C.Jones: J. Opt. Soc. Am.31, 488–493 (1941)Google Scholar
  10. 10.
    R.C.Jones: J. Opt. Soc. Am.31, 493–499 (1941)Google Scholar
  11. 11.
    R.C.Jones: J. Opt. Soc. Am.31, 500–503 (1941)Google Scholar
  12. 12.
    R.C.Jones: J. Opt. Soc. Am.32, 486–493 (1942)Google Scholar
  13. 13.
    R.C.Jones: J. Opt. Soc. Am.37, 107–110 (1947)Google Scholar
  14. 14.
    R.C.Jones: J. Opt. Soc. Am.37, 110–112 (1947)Google Scholar
  15. 15.
    R.C.Jones: J. Opt. Soc. Am.38, 671–685 (1948)Google Scholar
  16. 16.
    E.B.Wilson, J.C.Decius, P.C.Cross:Molecular Vibrations (McGraw-Hill, New York 1955)Google Scholar
  17. 17.
    P.R.Monson, W.M.McClain: J. Chem. Phys.53, 29–37 (1970)CrossRefGoogle Scholar
  18. 18.
    W.M.McClain: J. Chem. Phys.55, 2789–2796 (1971)CrossRefGoogle Scholar
  19. 19.
    P.R.Monson, W.M.McClain: J. Chem. Phys.56, 4817–4825 (1972)CrossRefGoogle Scholar
  20. 20.
    R.H.Harris, W.M.McClain, C.F.Sloane: Mol. Phys.28, 381–398 (1974)CrossRefGoogle Scholar
  21. 21.
    W.M.McClain: Acc. Chem. Res.7, 129–135 (1974)CrossRefGoogle Scholar
  22. 22.
    T.G.Spiro, T.C.Strekas: Proc. Nat. Acad. Sci.69, 2622–2626 (1972)CrossRefADSGoogle Scholar
  23. 23.
    M.Pézolet, L.A.Nafic, W.L.Peticolas: J. Raman Spectroscopy1, 455–464 (1973)CrossRefGoogle Scholar
  24. 24.
    J.Nestor, T.G.Spiro: J. Raman Spectroscopy1, 539–550 (1973)CrossRefGoogle Scholar
  25. 25.
    T.G.Spiro: Acc. Chem. Res.7, 339–344 (1974)CrossRefGoogle Scholar
  26. 26.
    E.L.Chang, W.G.Peticolas: Chem. Phys. Lett.40, 511–513 (1976)CrossRefADSGoogle Scholar
  27. 27.
    B.B.Berne, R.Pecora:Dynamic Light Scattering (Wiley-Interscience, New York 1976)Google Scholar
  28. 28.
    F.Perrin: J. Chem. Phys.10, 415–427 (1942)CrossRefGoogle Scholar
  29. 29.
    R.A.Harris, W.M.McClain: J. Chem. Phys.67, 265–268 (1977)CrossRefADSGoogle Scholar
  30. 30.
    R.A.Harris, W.M.McClain: J. Chem. Phys.67, 269–270 (1977)CrossRefADSGoogle Scholar
  31. 31.
    R.A.Harris, W.M.McClain: J. Chem. Phys.67, 271–273 (1977)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • T. W. Barrett
    • 1
  1. 1.Department of ChemistryUniversity of OregonEugeneUSA

Personalised recommendations