How does equation (16) follow from equation (14) in Kohn-Sham 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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