Potential distribution theorem inverse

The spirit of the Hohenberg-Kohn theorem is that the inverse statement is also true The external potential v(r) is uniquely determined by the ground-state electron density distribution, n(r). In other words, for two different external potentials vi(r) and V2(r) (except a trivial overall constant), the electron density distributions ni(r) and 2(r) must not be equal. Consequently, all aspects of the electronic structure of the system are functionals of n(r), that is, completely determined by the function (r). 

Standard theorem of electrostatics that states that the potential due to a charge distribution, at any point at a distance R from the center of charges, can be expanded in a series of terms in the inverse powers of R, called multipoles [7] ... 

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