Functional relations for the density functional exchange and correlation   functionals connecting functionals at three densities
  It is shown that the DFT exchange and correlation functionals satisfy an expression that couples exchange and correlation functionals and functional derivatives evaluated at three different densities and for two particle numbers. This equation can be used as a stringent test to check the internal self-consistency of approximations to the exchange and correlation functionals. 
Daniel P. Joubert
cond-mat.mtrl-sci