I am not sure I understand the exchange correlation energy functional well enough at the moment. The E_xc[n] functional is an integral whose the integrand is written as sum of contributions. Each contribution gives a better approximation and metaphorically said to be a rung on the ladder. LDA has a contribution containing only n(r), GCA a contribution with some function of the gradient of n(r),MGGA- the laplactian of n(r), hyper GGA and generalised RPA I don’t know what those are. Every rung, approximation has the previous approximations contained in it and adds a term to the integrand.