Understanding the Expression (16) in Kohn Sham Energy Expansion

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The discussion centers on the derivation of expression (16) in the context of Kohn-Sham energy expansion, specifically referencing a paper from SciELO. Participants highlight the transition from expression (14) to (16), emphasizing the role of the linear term in electron density and the simplification achieved by incorporating complexities into the exchange-correlation function. The conversation underscores the importance of understanding the Kohn-Sham equations for grasping these transitions in density functional theory.

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  • Kohn-Sham equations in density functional theory
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Can anyone help me understand how to arrive at the expression (16) in the following link?

http://www.scielo.br/scielo.php?scr...0103-50532009000700002&lng=en&nrm=iso&tlng=en

I don't see how it follows from insertion into (14), but I have seen exactly this transition happen several places in litterature. There is only a linear term in the electron density, since the Kohn Sham equations has been used to put all the nasty stuff into the exchange-correlation function (as far as I understand).
 
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Could you be more concrete about which term you don't understand?
 

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