Theoretica chimica acta

, Volume 68, Issue 4, pp 291–300 | Cite as

Atomic charges based on spherical harmonics expansion at the atomic centers

  • Sven Larsson
  • Manuel Braga
Article

Abstract

Molecular orbitals are expanded in spherical harmonics functions around atomic centers. The expansion coefficient is a function of the distance from the nucleus and the quotient between this function and a corresponding atomic orbital is almost constant in the core region. The square of the quotient is used as a definition of an atomic charge component. The erratic dependence on the type of basis functions in the Mulliken method is thereby avoided. The relationship between the new charge and the Mulliken population is investigated and a new invariant Mulliken population is suggested.

Key words

Atomic charges Spherical harmonics expansion Net populations Ab initio wave functions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mulliken, R. S.: Phys. Rev. 41, 66 (1932); J. Chem. Phys. 3, 573 (1935)Google Scholar
  2. 2.
    Coulson, C. A., Longuet-Higgins, H. C.: Proc. Roy. Soc. (London) A191, 39 (1947); A192, 16 (1947): A193, 447 (1948); A194, 456 (1948); A195, 188 (1948)Google Scholar
  3. 3.
    Mulliken, R. S.: J. Chem. Phys. 23, 1833 (1955); 36, 3428 (1962)Google Scholar
  4. 4.
    Kern, C. W., Karplus, M.: J. Chem. Phys. 40, 1374 (1964)Google Scholar
  5. 5.
    Bader, R. F. W., Preston, H. J. T.: Int. J. Quant. Chem. 3, 327 (1969), and further references thereinGoogle Scholar
  6. 6.
    Davidson, E. R.: J. Chem. Phys. 46, 3320 (1967)Google Scholar
  7. 7.
    Politzer, P., Harris, R. R.: J. Am. Chem. Soc. 92, 6451 (1970); Politzer, P., Mulliken, R. S.: J. Chem. Phys. 55, 5135 (1971)Google Scholar
  8. 8.
    Roby, K. R.: Mol. Phys. 27, 81 (1974)Google Scholar
  9. 9.
    Heinzmann, R., Ahlrichs, R.: Theoret. Chim. Acta (Berl.) 42, 33 (1976)Google Scholar
  10. 10.
    Hirschfeld, F. H.: Theoret. Chim. Acta (Berl.) 44, 129 (1977)Google Scholar
  11. 11.
    Larsson, S.; Theoret. Chim. Acta (Berl.) 49, 45 (1978). In this paper 0.66 on page 49, just below Eq. (12) should be replaced by 0.46Google Scholar
  12. 12.
    Guenzburger, D., Maffeo, B., Larsson, S.: Int. J. Quant. Chem. 12, 383 (1977); Braga, M., Larsson, S., Leite, J. R.: J. Am. Chem. Soc. 101, 3867 (1979); Larsson, S., Hehenberger, M., Correa de Mello, P.: Int. J. Quant. Chem. 18, 1271 (1980)Google Scholar
  13. 13.
    Coolidge, A. S.: Phys. Rev. 42, 189 (1932)Google Scholar
  14. 14.
    Barnett, M. P.: In: Methods in Computational Physics, Vol. 2, pp. 95–153. Alder et al. (eds.) New York and London: Academic Press 1963Google Scholar
  15. 15.
    Löwdin, P. O.: Adv. Physics 5, 1 (1956), esp. pp. 96–111Google Scholar
  16. 16.
    Calais, J. L.: Arkiv. Fysik 28, 539 (1965).Google Scholar
  17. 17.
    Hobson, E. W.: Theory of Spherical and Ellipsoidal Harmonics, Cambridge University Press 1931Google Scholar
  18. 18.
    Pitzer, R. M., Kern, C. W., Lipscomb, W. N.: J. Chem. Phys. 37, 267 (1962)Google Scholar
  19. 19.
    Rouzo, H. L., Silvi, B.: Int. J. Quant. Chem. 13 297 (1978)Google Scholar
  20. 20.
    Ramsey, N. F.: Phys. Rev. 78 699 (1950)Google Scholar
  21. 21.
    Nefedov, W. I.: Phys. Stat. Sol. 2, 904 (1962); Barinski, R. L., Nefedov, W. I.: In: Röntgenspektros-kopische Bestimmung der Atomladungen in Molekülen. Leipzig: Akademische Verlagsgesellschaft 1969Google Scholar
  22. 22.
    Hagström, S., Nordling, C., Siegbahn, K.: Z. Physik 178 439 (1964)Google Scholar
  23. 23.
    Coulson, C. A., Zauli, C.: Mol. Phys. 6, 525 (1963)Google Scholar
  24. 24.
    Gelius, U.: Phys. Script 9, 133 (1974)Google Scholar
  25. 25.
    van Duijneveldt, F. B.: RJ 945. IBM, San José, California, December 1971Google Scholar
  26. 26.
    Larsson, S.: Chem. Phys. Lett. 7, 165 (1970)Google Scholar
  27. 27.
    Roos, B., Siegbahn, P.: Theoret. Chim. Acta. (Berl.) 17, 209 (1970)Google Scholar
  28. 28.
    Huzinaga, S.: J. Chem. Phys. 54, 2283 (1971)Google Scholar
  29. 29.
    Larsson, S.: J. Chem. Phys. 58, 5049 (1973)Google Scholar
  30. 30.
    Laaksonen, L., Pyykkö, P., Sundholm, D.: Chem. Phys. Lett. 96, 1 (1983); Sundholm, D., Pyykkö, P., Laaksonen, L.: private communicationGoogle Scholar
  31. 31.
    Coulson, C. A.: Nature 221, 1106 (1969)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Sven Larsson
    • 1
  • Manuel Braga
    • 2
  1. 1.Department of ChemistryUniversity of LundLundSweden
  2. 2.Departamento de FísicaUniversidade Federal de PernambucoRecifeBrazil

Personalised recommendations