Density Functionals of Correlation Energy

The first and immediate definition of energy correlation may be given by the difference between the exact and Hartree-Fock (HF) total energy of a poly-electronic system (Senatore March, 1994)  

Instead, in density functional theory the correlation energy can be seen as the gain of the kinetic and electron repulsion energy between the full 

In this context, taking the variation of the correlation energy (4.463) respecting the coupling parameter A (Ou-Yang Levy, 1991 Nagy et al., 1999), 

When restrieting to atomic systems, i.e., assuming spherieal symmetry, and neglecting the last term of the correlation poterrtial eqrration above, believed to be small (Liu et al., 1999), the equation to be solved simply becomes  

Quantum Nanochemistry-Volume I Quantum Theory and Observability 

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