Approximation for the Valence Energy

The evaluation of E presents no difficulty, but there is another, simplified, and most useful form that catches our attention. 

In Thomas-Fermi theory, adoption of the simple central field model for neutral molecules at equihbrium leads to simple energy relations—well supported by SCF calculations [12]—such as = (Vne + 2Vnn)- Evidently, nothing of the like apphes to vaience but wc may well inquire how things are with 

The key is in the treatment of core-other core and core-other nucleus interactions. Simple approximations were presented in that matter to get Eq. (4.35). Assuming Gauss theorem— the potential is just as though all the core electronic charge 

Direct calculations [89] made for li electrons confirm the vahdity of Eq. (4.38). 

The first RHS term of Eq. (4.38) describes the repulsion between Nl, located at the point and aU the outer electrons. The second term describes the attraction between Nl and all the nuclei other than Z t- Equation (4.18) now becomes 

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