Theoretica chimica acta

, Volume 49, Issue 2, pp 151–160 | Cite as

Screened potential in π-electron systems and its application to the estimation of excitation energies

  • Kenji Yamaguchi
Original Investigations


A diagrammatic technique was developed for the estimation of the screened potential of π-electron systems. The screened potential was expanded in terms of the polarization propagators which were constructed from either the singlet,\(\hat \Gamma ^1 \), or triplet vertex part,\(\hat \Gamma ^3 \). These vertex parts correspond to the singlet or triplet excitations, respectively, in the Random Phase Approximation (RPA) containing exchange diagrams. The excitation energies were calculated by using the screened potential in the framework of RPA with exchange. The excitation energies of several conjugated molecules with or without a hetero atom are in agreement with the experimental data.

Key words

Screened potential Green's function π-Electron systems, excitation energies of ∼ 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ball, M., McLachlan, A. D.: Mol. Phys.7, 501 (1964)CrossRefGoogle Scholar
  2. 2.
    Rowe, D. J.: Rev. Mod. Phys.40, 153 (1968)CrossRefGoogle Scholar
  3. 3.
    Paldus, J., Čižek, J.: J. Chem. Phys.60, 149 (1974)CrossRefGoogle Scholar
  4. 4.
    Tanimoto, O., Toyoda, K.: Mol. Phys.24, 1257 (1972)CrossRefGoogle Scholar
  5. 5.
    Shibuya, T., McKoy, V.: Phys. Rev.A2, 2208 (1970)CrossRefGoogle Scholar
  6. 6.
    I'Haya, Y. J., Narita, S., Yamaguchi, K., Nakayama, M.: Progr. Theoret. Phys.55, 1685 (1976)CrossRefGoogle Scholar
  7. 7.
    Gutfreund, H., Little, W. A.: Phys. Rev.183, 68 (1969); J. Chem. Phys.50, 4468 (1969)CrossRefGoogle Scholar
  8. 8.
    Toyoda, K., Iwai, T., Tanimoto, O.: Progr. Theoret. Phys.54, 333 (1975)CrossRefGoogle Scholar
  9. 9.
    Cooper, I. L., Linderberg, J.: Mol. Phys.25, 265 (1973)CrossRefGoogle Scholar
  10. 10.
    Hedin, L.: Phys. Rev.A139, 796 (1965)CrossRefGoogle Scholar
  11. 11.
    Parr, R. G.: Quantum theory of molecular electronic structure. New York: Benjamin 1963Google Scholar
  12. 12.
    Coulson, C. A., Longuet-Higgins, H. C.: Proc. Roy. Soc. (London)A191, 39 (1947)CrossRefGoogle Scholar
  13. 13.
    Roothaan, C. C. J.: J. Chem. Phys.19, 1145 (1951)CrossRefGoogle Scholar
  14. 14.
    Jørgensen, P., Linderberg, J.: Intern. J. Quantum Chem.4, 587 (1970)CrossRefGoogle Scholar
  15. 15.
    Fetter, A. L., Walecka, J. D.: Quantum theory of many-particle systems. New York: McGraw-Hill 1971Google Scholar
  16. 16.
    Tanimoto, O., Shimada, K.: Mol. Phys.23, 745 (1972)CrossRefGoogle Scholar
  17. 17.
    Noziéres, P.: The theory of interacting Fermi systems. New York: Benjamin 1963Google Scholar
  18. 18.
    Kimura, K., Tsubomura, H., Nagakura, S.: Bull. Chem. Soc. Japan37, 1336 (1964)CrossRefGoogle Scholar
  19. 19.
    Karkowski, J.: Acta Phys. Polon.A37, 417 (1970)Google Scholar
  20. 20.
    Haugen, W., Traetteberg, M.: Acta Chem. Scand.20, 1726 (1966)CrossRefGoogle Scholar
  21. 21.
    Mosher, O. A., Flicker, W. M., Kuppermann, A.: J. Chem. Phys.59, 6502 (1973)CrossRefGoogle Scholar
  22. 22.
    Terasaka, T., Iijima, T., Fujimura, Y., Nakajima, T.: Bull. Chem. Soc. Japan46, 1301 (1973)CrossRefGoogle Scholar
  23. 23.
    Allinger, N., Tai, J. C., Stuart, T.: Theoret. Chim. Acta (Berl.)8, 101 (1967)CrossRefGoogle Scholar
  24. 24.
    Kimura, K., Nagakura, S.: Mol. Phys.9, 117 (1965)CrossRefGoogle Scholar
  25. 25.
    McGlynn, S. P., Azumi, T., Kinoshita, M.: Molecular spectroscopy of triplet state. New York: Prentice-Halt 1969Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Kenji Yamaguchi
    • 1
  1. 1.Department of ChemistryThe University of TsukubaIbarakiJapan

Personalised recommendations