Applicable Algebra in Engineering, Communication and Computing

, Volume 15, Issue 2, pp 101–128

Exchange Energy for Two-Active-Electron Diatomic Systems Within the Surface Integral Method

Authors

    • Zentralinstitut für Angewandte Mathematik (ZAM)Forschungszentrum Jülich GmbH
    • Theoretische ChemieFakultät für Chemie, Universität Bielefeld
  • M. Aubert-Frécon
    • LASIMCNRS et Université
  • D. Andrae
    • Theoretische ChemieFakultät für Chemie, Universität Bielefeld
  • J. Grotendorst
    • Zentralinstitut für Angewandte Mathematik (ZAM)Forschungszentrum Jülich GmbH
  • J.D. Morgan III
    • Department of Physics and AstronomyUniversity of Delaware
  • M.L. Glasser
    • Department of PhysicsClarkson University
Article

DOI: 10.1007/s00200-004-0156-6

Cite this article as:
Scott, T., Aubert-Frécon, M., Andrae, D. et al. AAECC (2004) 15: 101. doi:10.1007/s00200-004-0156-6

Abstract.

We have analyzed and reduced a general (quantum-mechanical) expression for the atom-atom exchange energy formulated as a five-dimensional surface integral, which arises in studying the charge exchange processes in diatomic molecules. It is shown that this five-dimensional surface integral can be decoupled into a three-dimensional integral and a two-dimensional angular integral which can be solved analytically using a special decomposition. Exact solutions of the two-dimensional angular integrals are presented and generalized. Algebraic aspects, invariance properties and exact solutions of integrals involving Legendre and Chebyshev polynomials are also discussed.

Keywords

Symbolic integrationNumerical integrationMolecular physicsSpecial functions and sumsAsymptotic series
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© Springer-Verlag Berlin Heidelberg 2004