Electronic prolate spheroidal orbitals for diatomic molecules
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.gitattributes
LICENSE.txt
README.md
carbon_monoxide.nb
carbon_monoxide_3sub.nb
diatomic_base.m
diatomic_coulomb_m0.nb
diatomic_coulomb_m0_base.m
diatomic_coulomb_m1.nb
diatomic_coulomb_m1_base.m
diatomic_coulomb_m2.nb
diatomic_coulomb_m2_base.m
heteronuclear_levels.nb
homonuclear_levels.nb
oxygen.nb
oxygen_delta.nb
oxygen_singlet.nb

README.md

Electronic prolate spheroidal orbitals for diatomic molecules

Mathematica notebooks computing electronic prolate spheroidal orbitals for diatomic molecules, i.e., solving the two-center single-electron Schrodinger equation, and calculating Coulomb and exchange integrals of these orbitals; see Ref. 1 and 2 for details. To run the notebooks, the FermiFab toolbox (Ref. 3) is required.

File structure

  • diatomic_base.m: Mathematica package defining the core computational routines
  • homonuclear_levels.nb: single-electron energy levels in dependence of Z*R, homonuclear case, where R is the nuclear distance (bond length) and Z the nuclear charge
  • heteronuclear_levels.nb: single-electron energy levels, heteronuclear case
  • diatomic_coulomb_m*.nb pre-computation of Coulomb integral tables
  • oxygen*.nb ground state energy of the O2 molecule for various symmetries, using the prolate spheroidal orbitals as single-electron basis
  • carbon_monoxide.nb ground state energy of the CO molecule

License

Copyright (c) 2011-2012, Christian B. Mendl
All rights reserved.
http://christian.mendl.net

This program is free software; you can redistribute it and/or modify it under the terms of the Simplified BSD License http://www.opensource.org/licenses/bsd-license.php

References

  1. Christian B. Mendl
    Efficient algorithm for two-center Coulomb and exchange integrals of electronic prolate spheroidal orbitals
    J. Comput. Phys. 231, 5157–5175 (2012), arXiv:1203.6256
  2. M. Aubert, N. Bessis and G. Bessis
    Prolate-spheroidal orbitals for homonuclear and heteronuclear diatomic molecules. I. Basic procedure
    Phys. Rev. A 10, 51–60 (1974) DOI
  3. Christian B. Mendl
    The FermiFab toolbox for fermionic many-particle quantum systems
    Comput. Phys. Commun. 182, 1327-1337 (2011), arXiv:1103.0872
    URL http://sourceforge.net/projects/fermifab