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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. Shull and P.O. Löwdin, J. Chem. Phys. 30 (1959) 617.
M. Rotenberg, Ann. Phys. (New York) 19 (1962) 62.
M. Rotenberg, Adv. At. Mol. Phys. 6 (1970) 233–268.
V.A. Fock, Z. Phys. 98 (1935) 145.
V.A. Fock, Kgl. Norske Videnskab Forh. 31 (1958) 138.
M. Bandar and C. Itzyksen, Rev. Mod. Phys. 38 (1966) 330, 346.
T. Shibuya and C.E. Wulfman, Proc. Roy. Soc. London Ser. A 286 (1965) 376.
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).
B.R. Judd, Angular Momentum Theory for Diatomic Molecules (Academic Press, New York, 1975).
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).
V. Aquilanti, S. Cavalli, C. Coletti and G. Grossi, Chem. Phys. 209 (1996) 405.
V. Aquilanti, S. Cavalli and C. Coletti, Chem. Phys. 214 (1977) 1.
J. Avery and D.R. Herschbach, Int. J. Quant. Chem. 41 (1992) 673.
N.K. Vilenkin, Special Functions and the Theory of Group Representations (American Mathematical Society, Providence, RI, 1968).
J. Avery, Hyperspherical Harmonics; Applications in Quantum Theory (Kluwer Academic, Dordrecht, 1989).
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.
E.J. Weniger, J. Math. Phys. 26 (1985) 276.
O. Goscinski, Preliminary research report No. 217, Quantum Chemistry Group, Uppsala University (1968).
J. Avery, Hyperspherical Harmonics and Generalized Sturmians (Kluwer Academic, Dordrecht, Netherlands, 2000).
V. Aquilanti and J. Avery, Chem. Phys. Lett. 267 (1997) 1.
J. Avery, J. Math. Chem. 21 (1997) 285.
J. Avery and F. Antonsen, J. Math. Chem. 24 (1998) 175.
J. Avery, Adv. Quantum Chem. 31 (1999) 201.
J. Avery, J. Mol. Struct. (Theochem) 458 (1999) 1.
J. Avery and R. Shim, Int. J. Quant. Chem. 79 (2000) 1.
J. Avery, J. Math. Chem. 24 (1998) 169.
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).
J. Avery and R. Shim, Int. J. Quant. Chem. 83 (2000) 1.
J. Avery, J. Math. Chem. 4 (2000) 279.
V. Aquilanti and J. Avery, Adv. Quant. Chem. 39 (2001) 71.
P.O. Löwdin, Appl. Phys. Suppl. 33 (1962) 251.
A.T. Amos and G.G. Hall, Proc. Roy. Soc. London Ser. A 263 (1961) 483.
H.F. King, R.E. Stanton, H. Kim, R.E. Wyatt and R.G. Parr, J. Chem. Phys. 47 (1967) 1936.
R. McWeeny, Methods of Molecular Quantum Mechanics, 2nd edn. (Academic Press, New York, 1992) pp. 61–66.
S. Rettrup, Notes for the Course KV-KK Quantum Chemistry (Chemistry Department, University of Copenhagen, 2002).
National Institute of Standards and Technology's Atomic Spectra Database, http://physics.nist.gov/asd
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Avery, J., Avery, J. The Generalized Sturmian Method for Calculating Spectra of Atoms and Ions. Journal of Mathematical Chemistry 33, 145–162 (2003). https://doi.org/10.1023/A:1023204016217
Issue Date:
DOI: https://doi.org/10.1023/A:1023204016217