Properties of the electron density p()is a non-negative function depending on only three variables .p()vanishes at infinity and integrates to the total number of electrons N: limp()=0 →0 p(di=N p()can be measured experimentally (e.g.by X-ray diffraction) at the position of atoms,the gradient of p()has a discontinuity: l层+2z6=0 Z being the nuclear charge and p()the spherical average of p() decays exponentially for large distances from nuclei p()~exp(-2v2) I being the exact first ionization energy of the system Function:y=f(x) p=p(xy,Z) Functional:y=F[f(x)] E=F[p(x,y,z)]Properties of the electron density Function: y=f(x) ρ = ρ(x,y,z) Functional: y=F[f(x)] E=F[ ρ(x,y,z)]