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

Scott, T. C.; Grotendorst, J.; Andrae, D.; Glasser, M. L.; Morgan III, J. D.; Aubert-Frécon, M.

doi:10.1007/s00200-004-0156-6

Journal Article

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

Scott, T. C. ; Aubert-Frécon, M. ; Andrae, D. ; Grotendorst, J.FZJ* ; Morgan III, J. D. ; Glasser, M. L.

2004
Springer Berlin

Applicable algebra in engineering, communication and computing 15, 101 - 128 (2004) [10.1007/s00200-004-0156-6]

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Please use a persistent id in citations: http://hdl.handle.net/2128/12067 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.

Keyword(s): J ; symbolic integration (auto) ; numerical integration (auto) ; molecular physics (auto) ; special functions and sums (auto) ; asymptotic series (auto)