Field Scaling for Diatomic Molecules

As stressed in Section 5, the first term of the 1/Z expansion of the total energy is the eigenvalue sum E for the Coulomb potential. In generalizing the 1/Z expansion to homonuclear diatomic molecules, one therefore needs, as the first term, the sum of the one-electron energies for the potential 

Therefore Dreizler and March have reported results for a large number of electrons (say 2TV), moving independently in the pure Coulomb potential (101), and present in the molecular ion. The asymptotic eigenvalue sum presented below, we must stress, will only be rigorously valid in the limit when Z and TV tend to infinity, in a non-relativistic framework. 

Teller and H. L. Shalin, Physical Chemistry , Academic Press, New York, 1970, Vol. 5. 

These then are the asymptotic scaling laws in a pure Coulomb field for two identical centres. We apply these results to scaling laws in molecules, including the interactions self-consistently below. 

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