Theoretica chimica acta

, Volume 48, Issue 3, pp 223–239 | Cite as

Violation of Hund's rule by spin polarization in molecules

  • H. Kollmar
  • V. Staemmler
Original Investigations


It is shown that spin polarization effects can lead to violations of Hund's multiplicity rule, particularly for singlet-triplet pairs. In systems with more than one unpaired electron we observe a dynamic spin polarization which depends on the relative spin orientation of the unpaired electrons and is different in open-shell singlet and triplet states. These effects are described by including singly substituted configurations in CI-type wavefunctions for the two states. In analyzing the contributions of the various singly substituted configurations a quantitative understanding of violations of Hund's rule is obtained; at the same time it is possible to calculate quantitatively spin polarization contributions to the correlation energies of open-shell singlet and triplet states.

A series of model calculations is performed on systems like square planar H4 and C4H4, nπ* states of formaldehyde, rotated cumulenes, NH and O2, in order to investigate how strongly spin polarization influences singlet-triplet energy splittings and what are the properties of a molecule that lead to a violation of Hund's multiplicity rule.

Key words

Spin polarization Hund's multiplicity rule Singlet-triplet energy splitting 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hund, F.: Linienspektren und periodisches System der Elemente, p. 124. Berlin: J. Springer 1927Google Scholar
  2. 2.
    Moore, C. E.: Atomic energy levels, National Bureau of Standard Circ. Nr. 467. Washington: U.S. Governm. Printing Office 1949Google Scholar
  3. 3.
    Salem, L.: Pure Appl. Chem. 33, 317 (1973)Google Scholar
  4. 4.
    Buenker, R. J., Peyerimhoff, S. D.: J. Chem. Phys. 48, 354 (1968)Google Scholar
  5. 5.
    Wilson, C. W., Goddard III, W. A.: J. Chem. Phys. 51, 716 (1969)Google Scholar
  6. 6.
    Rubinstein, M., Shavitt, I.: J. Chem. Phys. 51, 2014 (1969)Google Scholar
  7. 7.
    Silver, D. M., Stevens, R. M.: J. Chem. Phys. 59, 3378 (1973)Google Scholar
  8. 8.
    Buenker, R. J., Peyerimhoff, S. D.: Chem. Phys. 9, 75 (1975)Google Scholar
  9. 9.
    Merer, A. J., Mulliken, R. S.: Chem. Rev. 69, 639 (1969)Google Scholar
  10. 10.
    Shavitt, I.: private communication.Google Scholar
  11. 11.
    Borden, W. T.: J. Am. Chem. Soc. 97, 5968 (1975)Google Scholar
  12. 12.
    Yamaguchi, K.: Chem. Phys. Letters 35, 230 (1975)Google Scholar
  13. 13.
    Yamaguchi, K., Fueno, T.: Chem. Phys. 19, 35 (1977)Google Scholar
  14. 14.
    Colpa, J. P.: Mol. Phys. 28, 581 (1974)Google Scholar
  15. 15.
    Katriel, J.: Phys. Rev. A5, 1990 (1972)Google Scholar
  16. 16.
    Katriel, J.: Theoret. Chim. Acta (Berl.) 23, 309 (1972); 26, 163 (1972)Google Scholar
  17. 17.
    Jungen, M.: Theoret. Chim. Acta (Berl.) 11, 193 (1968)Google Scholar
  18. 18.
    Weissman, S. I.: J. Chem. Phys. 25, 890 (1956); McConnell, H. M., Chesnut, D. B.: J. Chem. Phys. 28, 107 (1958)Google Scholar
  19. 19.
    Memory, J. D.: Quantum theory of magnetic resonance parameters. New York, McGraw-Hill: 1968Google Scholar
  20. 20.
    Kollmar, H., Staemmler, V.: J. Am. Chem. Soc. 99, 3583 (1977)Google Scholar
  21. 21.
    Huzinaga, S.: Approximate atomic functions I. Preprint, University of Alberta, Canada 1971Google Scholar
  22. 22.
    Kollmar, H.: unpublished results.Google Scholar
  23. 23.
    Moule, D. C., Walsh, A. D.: Chem. Rev. 75, 67 (1975)Google Scholar
  24. 24.
    Herzberg, G.: Electronic spectra and electronic structure of polyatomic molecules. Princeton: Van Nostrand 1967Google Scholar
  25. 25.
    Huo, W. M.: J. Chem. Phys. 49, 1482 (1968)Google Scholar
  26. 26.
    Gilles, A., Masanet, J., Vermeil, C.: Chem. Phys. Letters 25, 346 (1974); Masanet, J., Gilles, A., Vermeil, C.: J. Photochem. 3, 417 (1974); Vermeil, C., Masanet, J., Gilles, A.: Intern. J. Radiat. Phys. Chem. 7, 275 (1975)Google Scholar
  27. 27.
    Zetsch, C., Stuhl, F.: Ber. Bunsenges, Phys. Chem. 80, 1348 (1976); 80, 1354 (1976)Google Scholar
  28. 28.
    Krupenie, P.: J. Phys. Chem. Ref. Data 1, 423 (1972)Google Scholar
  29. 29.
    Driessler, F., Ahlrichs, R., Staemmler, V., Kutzelnigg, W.: Theoret. Chim. Acta (Berl.) 30, 315 (1973)Google Scholar
  30. 30.
    Staemmler, V.: Habilitationsschrift, Bochum 1975Google Scholar
  31. 31.
    Diehl, H. P.: Diplom thesis, Bochum 1976Google Scholar
  32. 32.
    Jungen, M., Ahlrichs, R.: Theoret. Chim. Acta (Berl.) 17, 399 (1970)Google Scholar
  33. 33.
    Ahlrichs, R., Lischka, H., Staemmler, V., Kutzelnigg, W.: J. Chem. Phys. 62, 1225 (1975)Google Scholar
  34. 34.
    Ahlrichs, R., Driessler, F.: Theoret. Chim. Acta (Berl.) 36, 275 (1975)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • H. Kollmar
    • 1
  • V. Staemmler
    • 1
  1. 1.Lehrstuhl für Theoretische ChemieAbteilung für Chemie der Ruhr-Universität BochumBochumFederal Republic of Germany

Personalised recommendations