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The relation between the open shell energy functional in the Roothaan method and the symmetry of the system

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Abstract

The origin of terms not described in the Roothaan theory in molecular systems with one open shell is discussed. The appearance of these terms can be formally considered as a result of the splitting of the levels of the pN configuration of the atom (or the NπN of the linear molecule) in a low symmetry field. For the atomic shell of the pN state we obtained the concept of two-particle spinless density through the one-particle density, which allows the expression of the a and b coefficients in the corresponding Roothaan energy functional through the orbital and spin moments and the number of electrons.

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Literature cited

  1. C. C. J. Roothaan, “Self-consistent field theory for open shells of electronic systems,” Rev. Mod. Phys., 32, No. 2, 179–185 (1960).

    Google Scholar 

  2. S. Husinaga, “Analytical methods in Hartree-Fock self-consistent field theory,” Phys. Rev., 122, No. 1, 131–138 (1961).

    Google Scholar 

  3. A. A. Kiselev, “Theory of many-electron systems with unoccupied layers,” Vestn. Leningrad. Univ., No. 22, 5–12 (1962).

    Google Scholar 

  4. R. A. Evarestov, “Electronic energy for molecular systems with open shells,”2 Teor. Éksp. Khim., 18, No. 5, 515–520 (1982).

    Google Scholar 

  5. M. M. Mestechkin, G. T. Klimko, and V. A. Kuz'mitskii, “The basis of Roothaan's theory for an open shell,”2 Teor. Éksp. Khim., 20, No. 6, 641–649 (1984).

    Google Scholar 

  6. R. McWeen and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, New York (1969).

    Google Scholar 

  7. B. N. Plakhutin and G. M. Zhidomirov, “Construction of functions of correct symmetry for non-Roothaan type terms in the restricted Hartree-Fock method,” Zh. Strukt. Khim., 27, No. 2, 3–10 (1986).

    Google Scholar 

  8. G. T. Glimko, V. A. Kuz'mitskii, and M. M. Mestechkii, “1The restricted Hartree-Fock method for states of a system of open shell degenerate orbitals,” Abstract of Papers: Conference on Quantum Chemistry, Dnepropetrovsk (1983), p. 8–9.

  9. V. A. Kuz'mitskii, G. T. Klimko, M. M. Mestechkii, and V. N. Poltavets, “Calculation of the electronic structure of metalloporphyrin dianions by the restricted Hartree-Fock method,” Teor. Éksp. Khim., 22, No. 2, 153–160 (1986).

    Google Scholar 

  10. I. G. Kaplan, Symmetry of Many-electron Systems, Academic Press, New York (1975).

    Google Scholar 

  11. M. I. Petrashen' and E. D. Trifonov, The Application of Group Theory to Quantum Mechanics [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  12. J. Gerratt, “General theory of spin-coupled wave functions for atoms and molecules,” Adv. Atom. Mol. Phys., 7, 141–221 (1971).

    Google Scholar 

  13. H. A. Bethe, “Termauspaltung in Kristallen,” Ann. Phys., 3, No. 1, 133–208 (1929).

    Google Scholar 

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Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 23, No. 2, pp. 129–134, March–April, 1987.

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Plakhutin, B.N., Klimko, G.T., Mestechkin, M.M. et al. The relation between the open shell energy functional in the Roothaan method and the symmetry of the system. Theor Exp Chem 23, 123–128 (1987). https://doi.org/10.1007/BF00534571

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