Theoretica chimica acta

, Volume 58, Issue 2, pp 137–144 | Cite as

Some rules forS(-2k) dipole sums?

  • Jonathan A. Yoffe
  • Gerald M. Maggiora
  • A.Terry Amos
Original Investigations


Stieltjes conditions and the ratio test provide necessary but not sufficient conditions onS(-2k) dipole sums. If the dipole sums are accurate the associated [n, n −1] Padé approximant provides a better representation of α (Ω), the frequency-dependent dipole polarizability, than a truncated series expression and, in addition, should bound α(Ω) below. It is shown how constraints on the dipole sums effect the form of the [2,1] Padé approximant and an additional constraint is derived that ensures the analyticity of the approximant on 0≤ Ω < Ω1. There then follows a discussion of the reliability of available literature dipole sum values for small molecules containing H, C, N and O.

Key words

Dipole sums Padé approximants 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hirschfelder, J. O., Byers Brown, W., Epstein, S. T.: Advan. Quantum. Chem. 1, 255 (1964)Google Scholar
  2. 2.
    Langhoff, P. W., Karplus, M.: J. Opt. Soc. Am.59, 863 (1969)Google Scholar
  3. 3.
    Pack, R. T.: J. Chem. Phys.61, 2091 (1974)Google Scholar
  4. 4.
    Cummings, F. E.: J. Chem. Phys.63, 4960 (1975)Google Scholar
  5. 5.
    Starkschall, G., Gordon, R. G.: J. Chem. Phys.54, 663 (1971)Google Scholar
  6. 6.
    Dalgarno, A., Morrison, I. H., Pengelly, R. M.: Intern. J. Quantum Chem.1, 161 (1967)Google Scholar
  7. 7.
    Thomas, G. F., Meath, W. J.: A.I.Ch.E. J.25, 352 (1979)Google Scholar
  8. 8.
    Dalgarno, A., Kingston, A. E.: Proc. Roy. Soc.A259, 424 (1960)Google Scholar
  9. 9.
    Zeiss, G. D., Meath, W. J.: Mol. Phys.33, 1155 (1977)Google Scholar
  10. 10.
    Thomas, G. F., Meath, W. J.: Mol. Phys.34, 113 (1977)Google Scholar
  11. 11.
    Margenau, H.: Phys. Rev.37, 1425 (1931)Google Scholar
  12. 12.
    Margenau, H.: Phys. Rev.56, 1000 (1939)Google Scholar
  13. 13.
    Dalgarno, A., Kingston, A. E.: Proc. Phys. Soc.72, 1053 (1958)Google Scholar
  14. 14.
    Neilson, G. C., Parker, G. A., Pack, R. T.: J. Chem. Phys.64, 2055 (1976).Google Scholar
  15. 15.
    Parker, G. A., Pack, R. T.: J. Chem. Phys.64, 2010 (1976)Google Scholar
  16. 16.
    Gerhart, D. E.: J. Chem. Phys.62, 821 (1975).Google Scholar
  17. 17.
    Robin, M. B.: Higher excited states of polyatomic molecules, Vol. 1 New York: Academic Press 1974Google Scholar
  18. 18.
    Langhoff, P. W., Karplus, M. in: The Padé approximant in theoretical physics, G. A. Baker Jr. and J. L. Gammel, Eds., Chpt. 2. New York: Academic Press 1970Google Scholar
  19. 19.
    Shull, H., Hall, G. G.: Nature184, 1559 (1959)Google Scholar
  20. 20.
    Herzberg, G.: Spectra of diatomic molecules. New York: D. van Nostrand 1966Google Scholar
  21. 21.
    Herzberg, G.: Electronic spectra and electronic structure of polyatomic molecules. New York: D. van Nostrand. 1966Google Scholar
  22. 22.
    Margoliash, D. J., Meath, W. J.: J. Chem. Phys.68, 1426 (1978)Google Scholar
  23. 23.
    Ashfold, M. N. R., Macpherson, M. T., Simons, J. P.: Topics Curr. Chem.86, 1 (1979)Google Scholar
  24. 24.
    Rabalais, J. W., McDonald, J. M., Scherr, V., McGlynn, S. P.: Chem. Rev.71, 73 (1971)Google Scholar
  25. 25.
    Hall, R. I., Chutjian, A., Trajmar, S.: J. Phys.B6, L264 (1973)Google Scholar
  26. 26.
    Peyerimhoff, S. D., Buenker, R. J.: J. Chem. Phys.49, 2473 (1968), and references cited thereinGoogle Scholar
  27. 27.
    Hall, R. I., Chutjian, A., Trajmar, S.: J. Phys.B6, L365 (1973)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Jonathan A. Yoffe
    • 1
  • Gerald M. Maggiora
    • 1
  • A.Terry Amos
    • 2
  1. 1.Departments of Biochemistry and ChemistryUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of NottinghamUniversity ParkEngland

Personalised recommendations