Sensitivity of Calculated Wave Numbers of a Normal Coordinate Treatment to Assumed Molecular Geometry

  • Robert R. Hart
Part of the Developments in Applied Spectroscopy book series (DAIS, volume 4)


Normal coordinate treatments rarely include a consideration of the effect on the treatment of experimental uncertainties in bond lengths and interbond angles. At the same time, the agreement between calculated and observed wave numbers is taken as the major criterion of the validities of the potential-energy constants obtained, of the form of internuclear potential-energy function assumed, and of such band assignments as may have been based on the treatment. To help understand this effect, numerical results were obtained for the changes of calculated wave numbers resulting from small alterations in bond lengths and interbond angles. The molecules used were thirteen types of substituted methanes, for which potential-energy constants had previously been obtained in this laboratory. The use of such molecules also helps in understanding how seriously the common assumption of tetrahedral structure for substituted methanes affects the many normal coordinate treatments of them that have appeared in the literature. The significance of the unexpectedly large changes obtained for normal coordinate treatments of more complex and structurally less well-determined molecules is discussed.


Force Constant Internuclear Distance Structural Uncertainty Band Assignment Tetrahedral Structure 
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  1. 1.
    W. F. Edgell and L. Parts, J. Am. Chem. Soc. 78: 2358 (1956).CrossRefGoogle Scholar
  2. 2.
    T. Shimanouchi and I. Suzuki, J. Mol. Spectroscopy 6: 277 (1961).CrossRefGoogle Scholar
  3. 3.
    J.S. Ziomek and E. A. Piotrowski, J. Chem. Phys. 34: 1087 (1961).CrossRefGoogle Scholar
  4. 4.
    J. Overend and J. R. Scherer, J. Chem. Phys. 33: 446 (1960).CrossRefGoogle Scholar
  5. 5.
    A. G. Meister, S.E. Rosser, and F. F. Cleveland, J. Chem. Phys. 18: 346 (1950).CrossRefGoogle Scholar
  6. 6.
    J. P. Zeitlow, F.F. Cleveland, and A. G. Meister, J. Chem. Phys. 18: 1076 (1950).CrossRefGoogle Scholar
  7. 7.
    C.E. Decker, A.G. Meister, and F.F. Cleveland, J.Chem. Phys. 19: 784 (1951).CrossRefGoogle Scholar
  8. 8.
    P. F. Fenlon, F. F. Cleveland, and A. G. Meister, J, Chem. Phys. 19: 1561 (1951).CrossRefGoogle Scholar
  9. 9.
    P.R. McGee, F.F. Cleveland, A.G. Meister, C.E. Decker, and S.I. Miller, J. Chem. Phys. 21: 242 (1953).CrossRefGoogle Scholar
  10. 10.
    H. B. Weissman, R.B. Bernstein, S. E. Rosser, A.G. Meister, and F.F. Cleveland, J. Chem. Phys. 23: 544 (1955).CrossRefGoogle Scholar
  11. 11.
    R.R. Hart, Comparison of computer methods of solving the eigenvalue problem of molecular spectroscopy, J. Franklin Inst. 279: 1 (1965).CrossRefGoogle Scholar
  12. 12.
    R.R. Hart, R.W. Estin, and E.A. Piotrowski, General normal coordinate treatment program, filed with and obtainable from Quantum Chemistry Program Exchange (QCPE), Indiana University, Bloomington, Indiana; see also QCPE Newsletter, No. 8 (January 1965), and R. Hart, Spectroscopia Mol. 13: 2 (1964).Google Scholar
  13. 13.
    K. Ramaswamy, K. Sathianandan, and F.F. Cleveland, J. Mol. Spectroscopy 9: 107 (1962).CrossRefGoogle Scholar
  14. 14.
    G.W. Bethke and M.K. Wilson, J. Chem. Phys. 26: 1118 (1957).CrossRefGoogle Scholar
  15. 15.
    S. Sundaram and F. F. Cleveland, J. Chem. Phys. 32: 166 (1960).CrossRefGoogle Scholar
  16. 16.
    S. Brodersen, Some of the principal problems in the determination of the potential function, in: Molecular Spectroscopy, Butterworth’s, London (1962), pp. 27–32.Google Scholar
  17. 17.
    S. L. Miner, L.C. Aamodt, G. Dousmanis, C.H. Townes, and J. Kraitchman, J. Chem. Phys. 20: 1112 (1952).CrossRefGoogle Scholar
  18. 18.
    C.C. Costain, J. Chem. Phys. 29: 864 (1958).CrossRefGoogle Scholar
  19. 19.
    K. Sathianandan, K. Ramaswamy, and F. F. Cleveland, J. Mol. Spectroscopy 8: 470 (1962).CrossRefGoogle Scholar
  20. 20.
    K. Nakamoto, J. Fujita, R.A. Condrate, and Y. Morimoto, J. Chem. Phys. 39: 423 (1963).CrossRefGoogle Scholar

Copyright information

© Chicago Section of the Society for Applied Spectroscopy 1965

Authors and Affiliations

  • Robert R. Hart
    • 1
  1. 1.Illinois Institute of TechnologyChicagoUSA

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