The generalized Sturmian method The generalized Sturmian method makes use of basis sets that are solutions to an approximate wave equation with a weighted potential. The weighting factors are chosen in such a way as to make all the members of the basis set isoenergetic. In this chapter we will show that when the approximate potential is taken to be that due to the attraction of the bare nucleus, the generalized Sturmian method is especially well suited for the calculation of large numbers of excited states of few-electron atoms and ions. Using the method we shall derive simple closed-form expressions that approximate the excited state energies of ions. The approximation improves with increasing nuclear charge. The method also allows automatic generation of near-optimal symmetry adapted basis sets, and it avoids the Hartree-Fock SCF approximation. Programs implementing the method may be freely downloaded from our website, url{} [1].

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  1. Cancès, Eric (ed.); Friesecke, Gero (ed.); Helgaker, Trygve Ulf (ed.); Lin, Lin (ed.): Mathematical methods in quantum chemistry. Abstracts from the workshop held March 18--24, 2018 (2018)
  2. Avery, James Emil; Avery, John Scales: A chainlike relative coordinate system for few-particle problems (2017)
  3. Morales, Daniel A.: On the evaluation of integrals with Coulomb Sturmian radial functions (2016)
  4. Avery, James Emil; Avery, John Scales: Molecular integrals for Slater type orbitals using Coulomb Sturmians (2014)
  5. Colavecchia, F. D.: Accelerating spectral atomic and molecular collisions methods with graphics processing units (2014)
  6. Han, Weimin; Atkinson, Kendall; Zheng, Hao: Some integral identities for spherical harmonics in an arbitrary dimension (2012)
  7. Avery, James; Avery, John: The generalized Sturmian method (2011)
  8. Mitnik, Darío M.; Colavecchia, Flavio D.; Gasaneo, Gustavo; Randazzo, Juan M.: Computational methods for generalized Sturmians basis (2011)
  9. Avery, John Scales: Harmonic polynomials, hyperspherical harmonics, and atomic spectra (2010)
  10. Avery, James; Avery, John: Atomic core-ionization energies; approximately piecewise-linear and linear relationships (2009)
  11. Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco: Quantum and semiclassical spin networks: From atomic and molecular physics to quantum computing and gravity (2008)
  12. Avery, James; Avery, John: Generalized Sturmians and atomic spectra. (2006)
  13. Avery, James; Avery, John: The generalized Sturmian method for calculating spectra of atoms and ions (2003)
  14. Avery, John: The generalized Sturmian method and inelastic scattering of fast electrons (2000)