The Normal Coordinate Treatment for Molecules with C2v, C3v, and Oh Symmetry

  • John R. Ferraro
  • Joseph S. Ziomek


The selection rules for a molecule, based on a hypothetical model, were derived in Chapter 2. The normal modes of this model can be determined using the normal coordinate treatment (NCT) method, which also serves to check the frequency assignments for the model. This method, which illustrates a useful application of group theory, depends on the bond lengths and bond angles of the model. Knowledge of force constants (the restoring force between two atoms) is also necessary, and the molecule must possess a high degree of symmetry.


Force Constant Secular Equation Character Table Common Bond Angle Deformation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. B. Wilson, J. C. Decius, and P. C. Cross, Molecular Vibrations, McGraw-Hill, New York (1955).Google Scholar
  2. 2.
    N. B. Colthup, L. H. Daly, and S. E. Wiberley, Introduction to Infrared and Raman Spectroscopy, Academic Press, New York (1975).Google Scholar
  3. 3.
    A. G. Meister and F. F. Cleveland, Am. J. Phys., 14:13 (1946).CrossRefGoogle Scholar
  4. 4.
    S. M. Ferigle and A. G. Meister, J. Chem. Phys., 19:982 (1951).CrossRefGoogle Scholar
  5. 5.
    J. C. Decius, J. Chem. Phys., 17:1315 (1949).CrossRefGoogle Scholar
  6. 6.
    E. B. Wilson, J. Chem. Phys., 7:1047 (1939).CrossRefGoogle Scholar
  7. 7.
    E. B. Wilson, J. Chem. Phys., 9:76 (1941).CrossRefGoogle Scholar
  8. 8.
    A. G. Meister and F. F. Cleveland, Molecular Spectra, II, Pubis. Ill. Inst. Technol. (1948).Google Scholar
  9. 9.
    H. H. Claassen, J. Chem. Phys., 30:968 (1959).CrossRefGoogle Scholar
  10. 10.
    C. W. F. T. Pistorius, J. Chem. Phys., 29:1328 (1958).CrossRefGoogle Scholar
  11. 11.
    D. F. Heath and J. W. Linnett, Trans. Faraday Soc., 45:264 (1949).CrossRefGoogle Scholar
  12. 12.
    K. Venkateswarlu and S. Sundaram, Z. Physik. Chem., 9:174 (1956).CrossRefGoogle Scholar
  13. 13.
    K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds, J. Wiley & Sons, New York (1970).Google Scholar
  14. 14.
    P. N. Schatz, J. Chem. Phys., 29:481 (1958).CrossRefGoogle Scholar
  15. 15.
    J. W. Linnett, Quart. Revs. (London), 1:73 (1947).CrossRefGoogle Scholar
  16. 16.
    L. A. Woodward, Trans. Faraday Soc., 54:1271 (1958).CrossRefGoogle Scholar
  17. 17.
    C. W. F. T. Pistorius, J. Chem. Phys., 28:514 (1958).CrossRefGoogle Scholar
  18. 18.
    K. Venkateswarlu and S. Sundaram, J. Chem. Phys., 23:2365 (1955).CrossRefGoogle Scholar
  19. 19.
    S. Sundaram, J. Chem. Phys., 33:708 (1960).CrossRefGoogle Scholar
  20. 20.
    H. Stammreich and R. Forneris, Spec. Acta, 16:363 (1960).CrossRefGoogle Scholar
  21. 21.
    J. D. S. Goulden, A. Maccoll, and D. J. Milien, J. Chem. Soc., 1950:1635.Google Scholar
  22. 22.
    A. Maccoll, Proc. Roy. Soc. N. S. Wales, 77:130 (1943).Google Scholar
  23. 23.
    A. Sabatini, L. Sacconi, and V. Schettino, Inorg. Chem., 3:1775 (1964).CrossRefGoogle Scholar
  24. 24.
    P. LaBonville, J. R. Ferraro, M. C. Wall, and L. J. Basile, Coord. Chem. Rev. 7:257 (1972).CrossRefGoogle Scholar
  25. 25.
    L. J. Basile, J. R. Ferraro, P. LaBonville, and M. C. Wall, Coord. Chem. Rev., 11:21 (1973).CrossRefGoogle Scholar
  26. 26.
    J. Gaunt, Trans. Faraday Soc., 50:546 (1954).CrossRefGoogle Scholar
  27. 27.
    J. Hiraishi, I. Nakagawa, and T. Shimanouchi, Spec. Acta, 20:819 (1964).CrossRefGoogle Scholar
  28. 28.
    H. F. Shurvell, Canadian Spec., 12:1156 (1967).Google Scholar
  29. 29.
    G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand, New York (1950).Google Scholar
  30. 30.
    E. B. Wilson, Ann. Rev. Phys. Chem., 2:151 (1951).CrossRefGoogle Scholar
  31. 31.
    O. Redlich, Z. Phys. Chem. (B), 28:371 (1935).Google Scholar
  32. 32.
    J. B. Decius and E. B. Wilson, J. Chem. Phys., 19:1409 (1951).CrossRefGoogle Scholar
  33. 33.
    B. E. Crawford and S. R. Brinkley, J. Chem. Phys., 9:69 (1941).CrossRefGoogle Scholar
  34. 34.
    H. Kim, P. A. Souder, and H. H. Claassen, J. Mol. Spec., 26:46 (1968).CrossRefGoogle Scholar
  35. 35.
    S. Sundaram, F. Suszek, and F. F. Cleveland, J. Chem. Phys., 32:251 (1960).CrossRefGoogle Scholar
  36. 36.
    G. DeAlti, G. Costa, and V. Galasso, Spec. Acta, 20:965 (1964).CrossRefGoogle Scholar
  37. 37.
    M. Pariseau, E. Wu, and J. Overend, J. Chem. Phys., 39:217 (1963).CrossRefGoogle Scholar
  38. 38.
    J. S. Ziomek and E. A. Piotrowski, J. Chem. Phys. 34:1087 (1961).CrossRefGoogle Scholar
  39. 39.
    W. A. Yeranos, Bull. Soc. Chim. Belg., 74:414 (1965).CrossRefGoogle Scholar
  40. 40.
    J. H. Schachtschneider and R. G. Snyder, Spec. Acta, 19:117 (1963).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • John R. Ferraro
    • 1
  • Joseph S. Ziomek
    • 1
  1. 1.Argonne National LaboratoryUSA

Personalised recommendations