Derivation of Selection Rules

  • John R. Ferraro
  • Joseph S. Ziomek


The complete selection rules for nonlinear molecules of the point group T d of the type AB4 are presented in this chapter. The selection rules govern which bands will appear in the infrared and Raman spectra and will apply to any molecule with the above-mentioned symmetry. The selection rules for linear molecules of the point group C v are also presented. For the derivation of selection rules we have employed the notation of Meister, Cleveland, and Murray.(1)


Selection Rule Point Group Factor Group None None Internal Mode 
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  1. 1.
    A. G. Meister, F. F. Cleveland, and M. J. Murray, Am. J. Phys., 11:239 (1943).CrossRefGoogle Scholar
  2. 2.
    J. E. Rosenthal and G. M. Murphy, Rev. Mod. Phys., 8:317 (1936).CrossRefGoogle Scholar
  3. 3.
    S. M. Ferigle and A. G. Meister, Am. J. Phys., 20:421 (1952).CrossRefGoogle Scholar
  4. 4.
    S. Bhagavantam and T. Venkatarayudu, Proc. Ind. Acad. Sei., A9:224 (1939);Google Scholar
  5. 4a.
    S. Bhagavantam and T. Venkatarayudu, Proc. Ind. Acad. Sei., A13:543 (1941).Google Scholar
  6. 5.
    S. S. Mitra, Z. Kristallogr., 116S:149 (1961).CrossRefGoogle Scholar
  7. 6.
    R. S. Halford, J. Chem. Phys., 14:8 (1946).CrossRefGoogle Scholar
  8. 7.
    H. Winston and R. S. Halford, J. Chem. Phys., 17:607 (1949).CrossRefGoogle Scholar
  9. 8.
    D. F. Hornig, J. Chem. Phys., 16:1063 (1948).CrossRefGoogle Scholar
  10. 9.
    M. H. Brooker and D. E. Irish, Can. J. Chem., 48:1183 (1970).CrossRefGoogle Scholar
  11. 10.
    D. W. James and W. H. Leong, J. Chem. Phys., 49:5089 (1968).CrossRefGoogle Scholar
  12. 11.
    I. Nakagawa and J. L. Walter, J. Chem. Phys., 51:1389 (1969).CrossRefGoogle Scholar
  13. 12.
    R. W. C. Wyckoff, Crystal Structures, Vol. 2, Wiley-Interscience, New York (1964).Google Scholar
  14. 13.
    I. Nakagawa, Coord. Chem. Rev., 4:423 (1969).CrossRefGoogle Scholar
  15. 14.
    V. C. Sinclair, J. M. Robertson, and A. Mathieson, Acta Cryst. 3:251 (1950);CrossRefGoogle Scholar
  16. 14a.
    S. S. Mitra, Air Force Materials Laboratory Report, AFML-TR-66–203, Wright-Patterson AFB, Ohio (1966).Google Scholar
  17. 15.
    S. S. Mitra, “Infrared and Raman Spectra Due to Lattice Vibrations,” in Optical Properties of Solids, S. Nudelman and S. S. Mitra, Eds., Plenum Press. New York (1969), pp. 333–341.Google Scholar
  18. 16.
    J. W. Menary, Acta Cryst., 8:840 (1955).CrossRefGoogle Scholar
  19. 17.
    G. J. Palenik, Inorg. Chem., 6:503 (1967).CrossRefGoogle Scholar
  20. 18.
    R. G. Dickinson, J. Am. Chem. Soc., 44:1489 (1922).CrossRefGoogle Scholar
  21. 19.
    J. R. Durig, K. K. Lau, G. Nagarajan, M. Walker, and J. Bragen, J. Chem. Phys., 50:2130 (1969);CrossRefGoogle Scholar
  22. 19a.
    R. J. Havighurst, J. Am. Chem. Soc., 48:2113 (1926).CrossRefGoogle Scholar
  23. 20.
    N. F. M. Henry and K. Lonsdale (eds.), International Tables for X-Ray Crystallography, Vol. I, The Kynoch Press, Birmingham, England (1965).Google Scholar
  24. 21.
    D. M. Adams and D. C. Newton, “Tables for Factor Group and Point Group Analysis,” Beckman-RIIC Limited, Surley House, England, J. Chem. Soc., 1970:2822.Google Scholar
  25. 22.
    D. M. Adams, Coord. Chem. Rev. 10:183 (1973).CrossRefGoogle Scholar

Recent Correlation Bibliography

  1. 1.
    R. K. Khanna and C. W. Reimann, “Spectra-Physics,” Raman Technical Bulletin No. 3 (1970).Google Scholar
  2. 2.
    W. G. Fateley, N. T. McDevitt, and F. F. Bentley, Appl. Spectry., 25:155 (1971).CrossRefGoogle Scholar
  3. 3.
    W. G. Fateley, F. R. Dollish, N. T. McDevitt, and F. F. Bentley, Infrared and Raman Selection Rules for Molecular and Lattice Vibrations: The Correlation Method, Wiley-Interscience, New York (1972).Google Scholar
  4. 4.
    J. R. Ferraro and P. LaBonville, “Space Group Selection Rules,” Argonne National Laboratory, Argonne, Illinois (1971).Google Scholar
  5. 5.
    R. Kopelman, J. Chem. Phys., 47:2631 (1967).CrossRefGoogle Scholar
  6. 6.
    D. M. Adams and D. C. Newton, J. Chem. Soc., 1970:2822.Google Scholar
  7. 7.
    J. E. Bertie and J. W. Bell, J. Chem. Phys., 54:160 (1971).CrossRefGoogle Scholar
  8. 8.
    B. DeAngelis, R. E. Newnham, and W. B. White, Am. Mineralogist, 57:255 (1972).Google Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

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

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