Proposed Scaling in Self-consistent Field Theory

Proposed Scaling in Self-consistent Field Theory.—March and Parr have proposed an extension of the 1 fZ expansion for atoms, analogous to rearrangement (48), for the case of diatomic molecules. Introducing a scaled length X=RZ, they note first that from the above discussion of the bare Coulomb field one has 

Then they effect the generalization of equation (47) to homonuclear diatomics as 

This then is the general scaling proposed12 for homonuclear diatomic molecules with nuclear charge Z and N electrons. If one takes the limit N - Z of neutral molecules, then one obtains 

That the first, TF, term will scale as shown is already clear from the work of Hund32 and of Townsend and Handler.45 

As in the case of atoms, one can determine the individual components of the energy from this expression. Thus, using Feynman s theorem one can obtain the electron-nuclear potential energy as 

---