Density Functionals of Exchange-Correlation Energy

Another approach in questing exchange and correlation density functionals consists in finding them both at once in what was defined as exchange-correlation density functional (4.404). In this regard, following the Lee and Parr approach (Lee Parr, 1990), the simplest starting point is to rewrite the inter-electronic interaction potential 

Quantum Nanochemistty-Volume I Quantum Theory and Observability 

Inserting relations (4.496)-(4.503) in -J) difference it is eventually converted from the genuine exchange meaning into practical exchange-correlation energy characterized by the density fimctional form  

Making use of the two possible multiplication of the series in Eq. (4.504), i.e., either by retaining the a(r) containing function only or by including also the density gradient terms in the first curled brackets, thus retaining also the term containing (r) fimction, the so-called I-xc or ll-xc type Junctionals are respectively obtained. 

laying aside other variants and choosing the simple (however meaningfully) density dependency 

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