Abstract
The conditions applicable at the limits of the united atom and the separate atoms may be applied to any radial function for diatomic molecules based on the argument z≡2(R−Re)/ (R+Re) so as to generate further coefficients in a polynomial representation that thus has the correct asymptotic behavior in the approach to these limits. The appropriate conditions are given for the potential-energy and dipole-moment functions, and the results are illustrated by application to HCl. This type of representation is compared with rational functions.

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