Hellmann-Feynman theorem electronic kinetic energy

Derivation and integration of the above equation with respect to X will yield the difference of the energies of the real and noninteracting systems (E-Es) in the left hand side, and Es is exactly VS+TS) i.e., the sum of the potential energy plus the kinetic energy of a noninteractive system of electrons with density identical to the real system. Then using the Hellmann-Feynman theorem... 

The Laplacian of the charge density as it appears in the local expression of the virial theorem, eqn (7.4), compares twice the kinetic energy density C(r) not with contributions to the potential F, but with F, the electronic potential energy. This is an important distinction from the point of view of whether or not a system is bound. Consider an interaction where V p is predominantly negative over the binding region and net forces of attraction act on the nuclei. In this case the local contribution to the virial of the Hellmann-Feynman forces exerted on the electrons, which, as explained following eqn (6.60), is... 

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