Identity for the second functional derivative of the density functional   Hartree plus exchange-correlation functional
  It is shown that the integral of the product of the charge density difference of the N- and (N-1)-electron densities of the same Hamiltonian and the second functional derivative of the Hartree plus exchange-correlation functional of the N-electron density is equal to a constant. 
Daniel P. Joubert
cond-mat.mtrl-sci