Inclusion of Correlation in Density Theory

recognizing that from this theorem the exchange and correlation energy density, exc say, is a unique functional of the density, one now writes for the 

The Euler equation of the variation problem now involves the functional derivatives of the single-particle kinetic energy density tr corresponding to the exact many-body density p(r), and the exchange and correlation energy density exc. Such a minimization of equation (145) yields immediately 

Because of the definition of tr which was adopted, this has the form of singleparticle theory, but with potential energy71 72 

Evidently then equation (147) takes the approximate, but explicit, form 

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