The virial theorem and exact properties of density functionals for   periodic systems
  In the framework of density functional theory, scaling and the virial theorem are essential tools for deriving exact properties of density functionals. Preexisting mathematical difficulties in deriving the virial theorem via scaling for periodic systems are resolved via a particular scaling technique. This methodology is employed to derive universal properties of the exchange-correlation energy functional for periodic systems. 
H. Mirhosseini, A. Cangi, T. Baldsiefen, A. Sanna, C. R. Proetto, E.   K. U. Gross
cond-mat.other physics.chem-ph