[1] James Avery and John Avery. The generalized sturmian method for calculating spectra of atoms and ions. Journal of Mathematical Chemistry, 33:145-162, 2003. http://dx.doi.org/10.1023/A:1023204016217.
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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 Slater2013Condon 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.
[2] John Avery and James Avery. Kramers pairs in configuration interaction. Advances in Quantum Chemistry, 43:185-206, 2003.
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The theory of symmetry-preserving Kramers pair creation operators is reviewed and formulas for applying these operators to configuration interaction calculations are derived. A new and more general type of symmetry-preserving pair creation operator is proposed and shown to commute with the total spin operator and with all of the symmetry operations which leave the core Hamiltonian of a many-electron system invariant. The theory is extended to cases where orthonormality of orbitals of different configurations cannot be assumed.
[3] John Avery, James Avery, and Osvaldo Goscinski. Natural orbitals from generalized sturmian calculations. Advances in Quantum Chemistry, 43:206-216, 2003.
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The generalized Sturmian method is a direct configuration interaction method for solving the Schrödinger equation of a many-electron system. The configurations in the basis set are solutions to an approximate Schrödinger equation with a weighted potential βν V0(x), the weighting factors βν being chosen in such a way as to make the set of solutions isoenergetic. The method is illustrated by calculation of atomic excited states and used to generate natural orbitals.
[4] John Avery, James Avery, Vincenzo Aquilanti, and Andrea Caligiana. Atomic densities, polarizabilities, and natural orbitals derived from generalized sturmian calculations. Advances in Quantum Chemistry, 47:192-214, 2004.
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The generalized Sturmian method for atomic and molecular electronic structure calculations is a direct configuration interaction method in which the configurations are chosen to be isoenergetic solutions of an approximate N-electron Schrödinger equation with a weighted potential, βν V0. The weighting factors βν are especially chosen so that all the configurations in the basis set correspond to the same energy regardless of their quantum numbers. In this paper, the generalized Sturmian method is used to calculate excited states, densities, polarizabilities, and natural orbitals of few-electron atoms and ions.
[5] John Avery and James Avery. Generalized sturmian solutions for many-particle schrödinger equations. Journal of Physical Chemistry, 108:8848-8851, 2004. (Part of the Gert D. Billing Memorial Issue).
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[6] James Avery and John Avery. Autoionizing states of atoms calculated using generalized sturmians. Advances in Quantum Chemisty, 49:103-118, 2005.
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The generalized Sturmian method is applied to autoionizing states of atoms and ions. If the Goscinskian basis sets allow for a sufficient amount of angular correletion, the calculated energies of doubly-excited (autoionizing) states are found to agree well with the few available experimental energies. A large-Z approximation is discussed, and simple formulas are derived which are valid not only for autoionizing states, but for all states of an isoelectronic atomic series. Diagonalization of a small block of the interelectron repulsion matrix yields roots that can be used for a wide range of Z values.
[7] John Avery and James Avery. Generalized Sturmians and Atomic Spectra, chapter 4. Relativistic Effects. World Scientific, July 2006. Work in progress.
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[8] James Avery. Beregning af spektre for atomer og ioner ved brug af mangepartikel sturm-baser. Bachelor's project, Datalogisk Institut, KÝbenhavns Universitet, 2002.
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[9] John Avery. Hyperspherical Harmonics and Generalized Sturmians. Kluwer Academic Publishers, Dordrecht, Netherlands, 2000.
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[10] Osvaldo Goscinski. Preliminary research report no. 217. Advances in Quantum Chemistry, 41:51-85, 2003. Originally unpublished research report, Quantum Chemistry Group, Uppsala University, 1968.
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[11] National Institution of Standards and Technology. Atomic spectra database v.2.0. http://physics.nist.gov/asd.
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[12] James Avery. sturmian: The generalized sturmian library. http://sturmian.kvante.org, 2005.
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[13] John Avery. Many-center coulomb sturmians and shibuya-wulfman integrals. International Journal of Quantum Chemistry, 100(2):121-130, 2003.
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[14] John Avery. The generalized sturmian method and inelastic scattering of fast electrons. Journal of Mathematical Chemistry, 27(4):279-292, December 2000. ISSN: 0259-9791 (Paper) 1572-8897 (Online).
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[15] John Avery and Rune Shim. Molecular sturmians, part 1. International Journal of Quantum Chemistry, 83:1-10, 2001.
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[16] John Avery and Cecilia Coletti. Many-electron sturmians applied to atom and ions in strong external fields. New Trends in Quantum Systems in Chemistry and Physics, 1:77-93, 2001. Maruani et al. Eds. (Kluwer Academic Publishers).
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[17] John Avery and Cecilia Coletti. Generalized sturmians applied to atoms in strong external fields. Journal of Mathematical Chemistry, 27:43-51, 2000.
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[18] John Avery and Stephen Sauer. Many-electron sturmians applied to molecules. Quantum Systems in Chemistry and Physics, 1, 2000. A. HernŠndez-Laguna, J. Maruani, R. McWeeney and S. Wilson editors, Kluwer Academic Publishers.
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[19] John Avery. Many-electron sturmians applied to atoms and ions. Journal of Molecular Structure, 458:1-9, 1999.
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[20] John Avery. Many-electron sturmians as an alternative to the scf-ci method. Advances in Quantum Chemistry, 31:201-229, 1999.
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[21] John Avery and Frank Antonsen. Relativistic sturmian basis functions. Journal of Mathematical Chemistry, 24:175-185, 1998.
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[22] John Avery and Dudley Herschbach. Hyperspherical sturmian basis functions. International Journal of Quantum Chemistry, 41(5):673-686, 1992.
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[23] John Avery, Tom BÝrsen Hansen, Minchang Wang, and Frank Antonsen. Sturmian basis sets in momentum space. International Journal of Quantum Chemistry, 57(3):401-411, 1996.
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[24] Vincenzo Aquilanti, Simonetta Cavalli, Cecilia Coletti, D. Di Domenico, and G. Grossi. Hyperspherical harmonics as sturmian orbitals in momentum space: a systematic approach to the few-body coulomb problem. International Reviews in Physical Chemistry, 20(4):673-709, October 2001.
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[25] Vincenzo Aquilanti, Simonetta Cavalli, Cecilia Coletti, and G. Grossi. Alternative sturmian bases and momentum space orbitals: an application to the hydrogen molecular ion. Journal of Chemical Physics, 209:405-419, 1996.
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[26] Vincenzo Aquilanti, Andrea Caligiana, Simonetta Cavalli, and Cecilia Coletti. Hydrogenic orbitals in momentum space and hyperspherical harmonics: Elliptic sturmian basis sets. International Journal of Quantum Chemistry, 92(2), 2003.
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[27] Vincenzo Aquilanti and John Avery. Sturmian expansions for quantum mechanical many-body problems and hyperspherical harmonics. Advances in Quantum Chemistry, 39:72-101, 2001.
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[28] Vincenzo Aquilanti, Simonetta Cavalli, and Cecilia Coletti. The d-dimensional hydrogen atom: hyperspherical harmonics as momentum space orbitals and alternative sturmian basis sets. Chemical Physics, 214:1-13, 1997.
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[29] Vincenzo Aquilanti and Andrea Caligiana. Sturmian approach to one-electron many-center systems: integrals and iteration schemes. Chemical Physics Letters, 366:157-164, 2002.
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[30] Vincenzo Aquilanti and Andrea Caligiana. Sturmian orbitals and molecular structure. Journal of molecular structure (Theochem), 709:15-23, 2004.
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[31] Vincenzo Aquilanti and Andrea Caligiana. Sturmian orbitals in quantum chemistry: An introduction. Fundamental world of quantum chemistry: a tribute volume to the memory of Per-Olov LŲwdin, I:297-316, 2003. E. J. Bršndas and E. S. Kryachko (Eds.), Kluwer, Dordrecht.
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[32] Radoslaw Szmytkowski. Remarks on completeness of many-electron sturmians. J. Phys. A: Math. Gen., 33:4553-4559, 2000.
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[33] Radoslaw Szmytkowski. The dirac - coulomb sturmians and the series expansion of the dirac - coulomb green function: application to the relativistic polarizability of the hydrogen-like atom. J. Phys. B: At. Mol. Opt. Phys., 30:825-861, 1997.
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[34] Michaela Flock, Anne-Marie Kelterer, and Michael Ramek. Theoretical chemistry tutorial: Born-Oppenheimer approximation.
http://fptchlx03.tu-graz.ac.at/tc_tutorial/tcboE.html.
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[35] William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, NY, USA, 1992.
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[36] Wolfram Research. MathLink. http://www.wolfram.com/solutions/mathlink/mathlink.html. (Protocol and interface for communicating with Mathematica processes.).
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[37] Todd Gayley. A MathLink tutorial. http://library.wolfram.com/infocenter/TechNotes/174/, 1999.
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