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Journal of Mathematical Chemistry

, Volume 33, Issue 2, pp 145–162 | Cite as

The Generalized Sturmian Method for Calculating Spectra of Atoms and Ions

  • James Avery
  • John Avery
Article

Abstract

The properties of generalized Sturmian basis sets are reviewed, and functions of this type are used to perform direct configuration interaction calculations on the spectra of atoms and ions. Singlet excited states calculated in this way show good agreement with experimentally measured spectra. When the generalized Sturmian method is applied to atoms, the configurations are constructed from hydrogenlike atomic orbitals with an effective charge which is characteristic of the configuration. Thus, orthonormality between the orbitals of different configurations cannot be assumed, and the generalized Slater–Condon rules must be used. This aspect of the problem is discussed in detail. Finally spectra are calculated in the presence of a strong external electric field. In addition to the expected Stark effect, the calculated spectra exhibit anomalous states. These are shown to be states where one of the electrons is primarily outside the atom or ion, with only a small amplitude inside.

Keywords

Physical Chemistry Small Amplitude External Electric Field Effective Charge Atomic Orbital 
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.

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References

  1. [1]
    H. Shull and P.O. Löwdin, J. Chem. Phys. 30 (1959) 617.Google Scholar
  2. [2]
    M. Rotenberg, Ann. Phys. (New York) 19 (1962) 62.Google Scholar
  3. [3]
    M. Rotenberg, Adv. At. Mol. Phys. 6 (1970) 233–268.Google Scholar
  4. [4]
    V.A. Fock, Z. Phys. 98 (1935) 145.Google Scholar
  5. [5]
    V.A. Fock, Kgl. Norske Videnskab Forh. 31 (1958) 138.Google Scholar
  6. [6]
    M. Bandar and C. Itzyksen, Rev. Mod. Phys. 38 (1966) 330, 346.CrossRefGoogle Scholar
  7. [7]
    T. Shibuya and C.E. Wulfman, Proc. Roy. Soc. London Ser. A 286 (1965) 376.Google Scholar
  8. [8]
    C.E. Wulfman, Dynamical groups in atomic and molecular physics, in: Group Theory and Its Applications, ed. E.M. Loebel (Academic Press, New York, 1971).Google Scholar
  9. [9]
    B.R. Judd, Angular Momentum Theory for Diatomic Molecules (Academic Press, New York, 1975).Google Scholar
  10. [10]
    V. Aquilanti, S. Cavalli, D. De Fazio and G. Grossi, Hyperangular momentum: Applications to atomic and molecular science, in: New Methods in Quantum Theory, eds. C.A. Tsipis, V.S. Popov, D.R. Herschbach and J.S. Avery (Kluwer, Dordrecht, 1996).Google Scholar
  11. [11]
    V. Aquilanti, S. Cavalli, C. Coletti and G. Grossi, Chem. Phys. 209 (1996) 405.CrossRefGoogle Scholar
  12. [12]
    V. Aquilanti, S. Cavalli and C. Coletti, Chem. Phys. 214 (1977) 1.CrossRefGoogle Scholar
  13. [13]
    J. Avery and D.R. Herschbach, Int. J. Quant. Chem. 41 (1992) 673.Google Scholar
  14. [14]
    N.K. Vilenkin, Special Functions and the Theory of Group Representations (American Mathematical Society, Providence, RI, 1968).Google Scholar
  15. [15]
    J. Avery, Hyperspherical Harmonics; Applications in Quantum Theory (Kluwer Academic, Dordrecht, 1989).Google Scholar
  16. [16]
    J. Avery, Hyperspherical harmonics, some properties and applications, in: Conceptual Trends in Quantum Chemistry, Vol. 1, eds. E.S. Kryachko and J.L. Calais (Kluwer Academic, Dordrecht, Netherlands, 1994) pp. 135–169.Google Scholar
  17. [17]
    E.J. Weniger, J. Math. Phys. 26 (1985) 276.CrossRefGoogle Scholar
  18. [18]
    O. Goscinski, Preliminary research report No. 217, Quantum Chemistry Group, Uppsala University (1968).Google Scholar
  19. [19]
    J. Avery, Hyperspherical Harmonics and Generalized Sturmians (Kluwer Academic, Dordrecht, Netherlands, 2000).Google Scholar
  20. [20]
    V. Aquilanti and J. Avery, Chem. Phys. Lett. 267 (1997) 1.CrossRefGoogle Scholar
  21. [21]
    J. Avery, J. Math. Chem. 21 (1997) 285.CrossRefGoogle Scholar
  22. [22]
    J. Avery and F. Antonsen, J. Math. Chem. 24 (1998) 175.CrossRefGoogle Scholar
  23. [23]
    J. Avery, Adv. Quantum Chem. 31 (1999) 201.Google Scholar
  24. [24]
    J. Avery, J. Mol. Struct. (Theochem) 458 (1999) 1.CrossRefGoogle Scholar
  25. [25]
    J. Avery and R. Shim, Int. J. Quant. Chem. 79 (2000) 1.CrossRefGoogle Scholar
  26. [26]
    J. Avery, J. Math. Chem. 24 (1998) 169.CrossRefGoogle Scholar
  27. [27]
    J. Avery and S. Sauer, Many-electron Sturmians applied to molecules, in: Quantum Systems in Chemistry and Physics, Vol. 1, eds. A. Hernández-Laguna, J. Maruani, R. McWeeney and S. Wilson (Kluwer Academic, 2000).Google Scholar
  28. [28]
    J. Avery and R. Shim, Int. J. Quant. Chem. 83 (2000) 1.CrossRefGoogle Scholar
  29. [29]
    J. Avery, J. Math. Chem. 4 (2000) 279.CrossRefGoogle Scholar
  30. [30]
    V. Aquilanti and J. Avery, Adv. Quant. Chem. 39 (2001) 71.Google Scholar
  31. [31]
    P.O. Löwdin, Appl. Phys. Suppl. 33 (1962) 251.Google Scholar
  32. [32]
    A.T. Amos and G.G. Hall, Proc. Roy. Soc. London Ser. A 263 (1961) 483.Google Scholar
  33. [33]
    H.F. King, R.E. Stanton, H. Kim, R.E. Wyatt and R.G. Parr, J. Chem. Phys. 47 (1967) 1936.Google Scholar
  34. [34]
    R. McWeeny, Methods of Molecular Quantum Mechanics, 2nd edn. (Academic Press, New York, 1992) pp. 61–66.Google Scholar
  35. [35]
    S. Rettrup, Notes for the Course KV-KK Quantum Chemistry (Chemistry Department, University of Copenhagen, 2002).Google Scholar
  36. [36]
    National Institute of Standards and Technology's Atomic Spectra Database, http://physics.nist.gov/asdGoogle Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • James Avery
    • 1
  • John Avery
    • 2
  1. 1.Institute of Computer ScienceUniversity of CopenhagenCopenhagenDenmark
  2. 2.H.C. Ørsted InstituteUniversity of CopenhagenCopenhagenDenmark

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