That is, is the following statement true of approximate density functionals? What about for the exact density functional? $$ E_{xc}[\rho]=E_{xc}[\rho_A]+E_{xc}[\rho_B] $$ where, $$ \rho=\rho_A+\rho_B $$ $\rho_A$ and $\rho_B$ here are two arbitrary electron densities. I suspect this is not true in...