In order to improve approximations to density functionals such as the excha
nge-correlation functional, E-xc[rho], and the independent Fermion kinetic
energy functional, T-s[rho], it is essential to have information on the beh
avior of the exact functionals. Any approximation should then be made to sa
tisfy these conditions. With this in mind, constraints on functionals and f
unctional derivatives which reflect stability against translation, rotation
and uniform scaling of the charge density for electrons moving in a fixed
external potential, are derived from the minimal property of the energy fun
ctional F[rho] = T-s[rho] + U[rho] + E-xc[rho] when evaluated at a upsilon-
representable density rho(r). (C) 1999 American Institute of Physics. [S002
1-9606(99)01904-2].