The Application of Spectral Data from Isotopically Substituted Molecules to the Determination of Anharmonic Potential Energy Constants

  • Robert R. Hart
Part of the Developments in Applied Spectroscopy book series (DAIS, volume 5)


Attempts to obtain the anharmonic terms in the power-series expansion of a molecule’s internuclear force field encounter two difficulties. Firstly, these terms are much more numerous than the harmonic (quadratic) terms determined by the usual normal coordinate treatment. Secondly, data from isotopically substituted analogues are rarely used to characterize the force field common to both the molecule and its analogues; this further increases the paucity of data. The reason such data are not used, despite their being routinely employed in obtaining quadratic constants in the usual normal-coordinate treatment, is that the computations involved in the anharmonic case are much more difficult, The present investigation explores the possibility of carrying out such computations with the aid of an electronic computer to reduce computational difficulties, In addition, a systematic method is described for approximately characterizing the anharmonicities when insufficient data are available for their complete determination, which is the usual case. This method, in a sense, allows the molecule itself to state which of the anharmonic constants are the most important. The limited data available may then be used to determine these, while the less important anharmonic constants are set equal to zero. The method was tested by using solely the nine observed fundamental wave numbers of H2O, HDO, and D2O to characterize the force field common to all three molecules, which field involves four quadratic, six cubic, and nine quartic force constants. Reasonably good values of the harmonic wave numbers and of the principal anharmonicities are obtained.


Quartic Term Quadratic Case Vibrational Energy Level Anharmonic Term Anharmonic Constant 
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Copyright information

© Chicago Section of the Society for Applied Spectroscopy 1966

Authors and Affiliations

  • Robert R. Hart
    • 1
    • 2
  1. 1.Spectroscopy Laboratory Department of PhysicsIllinois Institute of TechnologyChicagoUSA
  2. 2.Bell Telephone Laboratories, Inc.Murray HillUSA

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