Theoretical and Experimental Chemistry

, Volume 22, Issue 4, pp 377–383 | Cite as

Instability of closed-shell Hartree-Fock solutions within the framework of the geminal approach

  • P. Karadakov
  • O. Kastan'o


The universal instability of the closed-shell Hartree-Fock solution within the framework of the approach in which the wave function is approximated by an antisymmetrized product of geminals was proved. It was shown that these results are applicable to the Goddard Gl-function method, the generalized valence bonds method, and also the Smeyers gamma-function method.


Wave Function Valence Bond Bond Method Antisymmetrized Product Generalize Valence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    J. A. Pople and R. K. Nesbet, “Self-consistent orbitals for radicals,” J. Chem. Phys., 22, No. 3, 571–572 (1954).Google Scholar
  2. 2.
    G. Berthier, “Configurations electronique incomplètes. 1. La méthode du moléculaire self-consistent et l'étude des états à couches incomplètes,” J. Chim. Phys., 51, No. 7/8, 363–371 (1954).Google Scholar
  3. 3.
    P. O. Löwdin, “Quantum theory of many-particle systems. 3. Extension of the HartreeFock scheme to include degenerate systems and correlation effects,” Phys. Rev., 97, No. 6, 1509–1520 (1955).Google Scholar
  4. 4.
    P. O. Löwdin, “The projected Hartree-Fock method. An extension of the independent particle scheme,” in: Quantum Theory of Atoms, Molecules, and the Solid State, Academic Press, New York (1966), pp. 601–623.Google Scholar
  5. 5.
    I. Mayer, “The spin-projected extended Hartree-Fock method,” Adv. Quant. Chem., 12, 189–262 (1980).Google Scholar
  6. 6.
    Y. G. Smeyers, “Etude d'une fonction unrestricted — Hartree-Fock ameliorée,” Anal. Fis., 67, No. 1/2, 17–24 (1971).Google Scholar
  7. 7.
    Y. G. Smeyers and A. M. Brucena, “Half-projected Hartree-Fock model for computing potential energy surfaces,” Int. J. Quant. Chem., 14, No. 5, 641–648 (1978).Google Scholar
  8. 8.
    J. Cizek and J. Paldus, “Stability conditions for the solutions of the Hartree-Fock equations for atomic and molecular systems. Application to the pi-electron model of cyclic polyenes,” J. Chem. Phys., 47, No. 10, 3976–3985 (1967).Google Scholar
  9. 9.
    J. Paldus and J. Cizek, “Stability conditions for the solutions of the Hartree-Fock equations for atomic and molecular systems. 6. Singlet-type instabilities and chargedensity wave Hartree-Fock solutions for cyclic polyenes,” Phys. Rev., A2, No. 6, 2268–2283 (1970).Google Scholar
  10. 10.
    H. Fukutome, “Unrestricted Hartree-Fock theory and its applications to molecules and chemical reactions,” Int. J. Quant. Chem., 20, No. 5, 955–1065 (1981).Google Scholar
  11. 11.
    M. M. Mestechkin, “Restricted Hartree-Fock method instability,” Int. J. Quant. Chem., 13, No. 3, 469–481 (1978).Google Scholar
  12. 12.
    P. Karadakov and O. Castano, “Stability properties of closed-shell restricted HartreeFock solutions for electronic systems in the framework of the projected Hartree-Fock method and their utilization,” Int. J. Quant. Chem., 24, No. 5, 453–477 (1983).Google Scholar
  13. 13.
    V. A. Fock, M. G. Veselov, and M. I. Petrashen', “Incomplete separation of variables for divalence atoms,” Zh. Eksp. Teor. Fiz., 10, No. 7, 723–739 (1940).Google Scholar
  14. 14.
    V. A. Fock, “Application of two-electron functions to the theory of chemical bonds,” Dokl. Akad. Nauk SSSR, 73, No. 4, 735–738 (1950).Google Scholar
  15. 15.
    A. C. Hurley, J. Lennard-Jones, and J. A. Pople, “The molecular orbital theory of chemical valency. 16. A theory of paired electrons in polyatomic molecules,” Proc. R. Soc. London, Ser. A, 220, 446–455 (1953).Google Scholar
  16. 16.
    J. E. Parks and R. G. Parr, “Theory of separated electron pairs,” J. Chem. Phys., 28, No. 2, 335–345 (1958).Google Scholar
  17. 17.
    D. M. Silver, E. L. Mehler, and K. Ruedenberg, “Electron correlation and separated pair approximation in diatomic molecules. 1. Theory,” J. Chem. Phys., 52, No. 3, 1174–1180 (1970).Google Scholar
  18. 18.
    E. L. Mehler, K. Ruedenberg, and D. M. Silver, “Electron approximation and separated pair approximation in diatomic molecules. 2. Lithium hydride and boron hydride,” J. Chem. Phys., 52, No. 3, 1181–1205 (1970).Google Scholar
  19. 19.
    W. Kutzelnigg, “Electron correlation and electron pair theories,” Fortschr. Chem. Forsch., 41, 31–73 (1973).Google Scholar
  20. 20.
    W. Kutzelnigg, “Pair correlation theories,” in: Modern Theoretical Chemistry, Plenum Press, New York (1977), pp. 129–188.Google Scholar
  21. 21.
    W. A. Goddard, “Improved quantum theory of many-electron systems. 2. The basic method,” Phys. Rev., 157, No. 1, 81–93 (1967).Google Scholar
  22. 22.
    F. M. Bobrowicz and W. A. Goddard, “The self-consistent field equations for generalized valence bond and open-shell Hartree-Fock wave functions,” in: Modern Theoretical Chemistry, Plenum Press, New York (1977), Vol. 3, pp. 79–127.Google Scholar
  23. 23.
    Y. G. Smeyers, G. Delgado-Barrio, L. Doreste-Suarez, et al., Theochemistry, 120, 431–436 (1985).Google Scholar
  24. 24.
    L. Doreste-Suarez, G. Delgado-Barrio, Y. G. Smeyers, et al., Theochemistry, 120, 437–441 (1985).Google Scholar
  25. 25.
    A. Hibbert and C. A. Coulson, “Saddle-point character of the Hartree-Fock energy,” Proc. Phys. Soc. London, 92, No. 1, 17–22 (1967).Google Scholar
  26. 26.
    C. A. Coulson, “Further note on the saddle-point character of the Hartree-Fock wave functions,” Acta Phys. Acad. Sci. Hung., 27, 345–349 (1969).Google Scholar
  27. 27.
    E. G. Larson, “Stability of a restricted Hartree-Fock-like wave function under the removal of a symmetry restriction,” Int. J. Quant. Chem. Symp., 2, 83–87 (1968).Google Scholar
  28. 28.
    K. Hirao and H. Nakatsuji, “Cluster expansion of the wave-function structure of the closed-shell orbital theory,” J. Chem. Phys., 69, No. 10, 4535–4547 (1978).Google Scholar
  29. 29.
    K. Hirao and H. Nakatsuji, “Cluster expansion of the wave function. The open-shell orbital theory including electron correlation,” J. Chem. Phys., 69, No. 10, 4548–4563 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • P. Karadakov
    • 1
  • O. Kastan'o
    • 1
  1. 1.Institute of Organic Chemistry, Bulgarian Academy of SciencesUniversity of SofiaSofia

Personalised recommendations