Generalized gradient approximations to density functional theory:   comparison with exact results
  In order to assess the accuracy of commonly used approximate exchange-correlation density functionals, we present a comparison of accurate exchange and correlation potentials, exchange energy densities and energy components with the corresponding approximate quantities. Four systems are used as illustrative examples: the model system of two electrons in a harmonic potential and the He, Be and Ne atoms. A new ingredient in the paper is the separation of the exchange-correlation potential into exchange and correlation according to the density functional theory definition. 
Claudia Filippi (Cornell University), Xavier Gonze (Universit\'e   Catholique de Louvain, Belgium), C. J. Umrigar (Cornell U...