Despite being size-extensive, the "second-generation" 1-matrix functionals for the electron-electron repulsion energy V-ee yield vanishing correlation energy for the homogeneous electron gas. This failure is directly related to the idempotency condition imposed upon an auxiliary matrix that enters the expression for V-ee. In particular, the recently proposed Kollmar-Hess functional is not volume-extensive and thus is incapable of properly describing any delocalized system at its thermodynamic limit. (C) 2004 American Institute of Physics.