Exchange Energy for Two-Active-Electron Diatomic Systems Within the Surface Integral Method
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- Scott, T., Aubert-Frécon, M., Andrae, D. et al. AAECC (2004) 15: 101. doi:10.1007/s00200-004-0156-6
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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.