Summary
In the so-called one-centre model of molecules CH4, the protons are smeared uniformly over the surface of a sphere of radiusR equal to the C—H bond length. Here the classical Runge-Lenz vector for the Kepler problem is generalized to this model. Our result reduces to the usual one in the united atom limitR → 0.
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References
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Kozlowski, P.M., March, N.H. Generalization of Coulomb classical Runge-Lenz vector to central field model of molecules CH4, SiH4, etc. Nuov Cim B 105, 1291–1296 (1990). https://doi.org/10.1007/BF02742684
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DOI: https://doi.org/10.1007/BF02742684