The Many Symmetries of Hubbard Alternant Polyenes

  • F. A. Matsen


In the freeon unitary-group-formulation of quantum chemistry the relevant group is U(n) where n is the number of freeon orbitals. The Hamiltonian is a second degree polynomial in the U(n) generators so the Hilbert space of the Hamiltonian is the direct sum of the U(n) irreducible representation spaces (IRS). The Pauli principle is imposed by restricting the physically significant IRS to those labeled by the partitions [λ] = [2(N/2)-S,12S] where N is the number of electrons and S is the spin. The IRS have the following properties: i) For each IRS labeled by [λ] there exists a conjugate IRS labeled by [λ] = [2(N/2)-S,12S] where N = 2n-N is the number of holes in [λ]. ii) The dimension of the [λ]th IRS equals the dimension of the [λ]th IRS. iii) The symmetry-adaptation of the [λ]th IRS with respect to any group yields the same decomposition as does the symmetry-adaptation of the [λ]th IRS. iv) There is defined a selfconjugate Hamiltonian such that the [λ]th and the [λ]th spectra differ by only a constant energy shift, ΔE = ΔE°(n-N). v) For n = N the conjugate group Gk, is a group of the Hamiltonian and supplies the conjugation quantum number.


Pauli Principle Primary Space Conjugate Space Baryon Octet Conjugate Group 
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  1. 1.
    F. A. Matsen, Int. J. Quantum Chem. 8S: 379 (1974)Google Scholar
  2. F. A. Matsen, Adv. Quantum Chem. (1978)Google Scholar
  3. F. A. Matsen and R. Pauncz, “The Unitary Group in Quantum Chemistry,” Elsevier, Amsterdam (in press).Google Scholar
  4. 2.
    J. Paldus, J. Chem. Phys. 61: 5321 (1974)CrossRefGoogle Scholar
  5. J. Paldus, “Theoretical Chemistry, Advances and Perspectives,” 2:131, Academic Press (1976).Google Scholar
  6. 3.
    I. M. Gel’fand and M. I. Graev, Am. Math. Soc. Translation 64: 116 (1964).Google Scholar
  7. 4.
    M. Moshinsky, J. Math. Phys. 4: 1128 (1963)CrossRefGoogle Scholar
  8. M. Moshinsky, “Group Theory and the Many-Body Problem,” Gordon and Breach (1968).Google Scholar
  9. 5.
    G. Baird and L. C. Biedenharn, J. Math. Phys. 4: 463 (1963).CrossRefGoogle Scholar
  10. 6.
    F. A. Matsen and T. L. Welsher, Int. J. Quantum Chem. 12: 985, 1001 (1977).CrossRefGoogle Scholar
  11. 7.
    J. Nagel and M. Moshinsky, J. Math. Phys. 6: 683 (1965)CrossRefGoogle Scholar
  12. J. Nagel and M. Moshinsky, Rev. Mexicana de Fis. 14: 29 (1965).Google Scholar
  13. 8.
    J. Koutecky, J. Paldus and J. Cizek, J. Chem. Phys. 83: 1722 (1985).CrossRefGoogle Scholar
  14. 9.
    A. D. McLachlan, Mol. Phys. 2:271 (1959)CrossRefGoogle Scholar
  15. 10.
    D. R. Herrick, Adv. Chem. Phys. 52: 1 (1983).CrossRefGoogle Scholar
  16. 11.
    L. Cizek, R. Pauncz and E. R. Vrscay, J. Chem. Phys. 78: 2486 (1983).Google Scholar
  17. 12.
    G. H. Shorley and B. Fried, Phys. Rev. 54: 739 (1938).CrossRefGoogle Scholar
  18. 13.
    D. Kurath, Phys. Rev. 101: 216 (1956).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • F. A. Matsen
    • 1
  1. 1.Departments of Chemistry and PhysicsThe University of TexasAustinUSA

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