Understanding the Expression (16) in Kohn Sham Energy Expansion

[aaaa202]

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).

 

[DrDu]

Could you be more concrete about which term you don't understand?