Formula for the Valence Region Energy

At this point we have all the required tools for deriving E.  

Up to now, potential energies were at the center of our arguments. Little attention was paid to the electronic kinetic energy. This situation arose from our application of the Helhuann-Feynman theorem with intent to stress the role of the potential 

We begin with Eq. (4.1) and write, with Eqs. (4.16)-(4.18) in mind, the following equation  

The latter equation achieves a separation of the core and valence contributions. The terms in brackets are individually zero at the hmits = 0 and N = 0. Here we postulate that physically meaningful core populations exist that allow such a core-valence separation and proceed with 

This formula can be simplified. The first term on its RHS is = Vne — specifically, the total nuclear-electronic potential energy of the molecule [Eq. (4.5)] stripped of all the individual core nuclear-electronic interactions V. Next, we decompose V  

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