Applicable Algebra in Engineering, Communication and Computing

, Volume 15, Issue 2, pp 101-128

First online:

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

  • T.C. ScottAffiliated withZentralinstitut für Angewandte Mathematik (ZAM), Forschungszentrum Jülich GmbHTheoretische Chemie, Fakultät für Chemie, Universität Bielefeld Email author 
  • , M. Aubert-FréconAffiliated withLASIM, CNRS et Université
  • , D. AndraeAffiliated withTheoretische Chemie, Fakultät für Chemie, Universität Bielefeld
  • , J. GrotendorstAffiliated withZentralinstitut für Angewandte Mathematik (ZAM), Forschungszentrum Jülich GmbH
  • , J.D. Morgan IIIAffiliated withDepartment of Physics and Astronomy, University of Delaware
  • , M.L. GlasserAffiliated withDepartment of Physics, Clarkson University

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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.


Symbolic integration Numerical integration Molecular physics Special functions and sums Asymptotic series