1 Hohenberg-Kohn theorems

Density functional theory relies on the theorems of Hohenberg and Kohn [144]. These two theorems could be summarized in the following: (I) That the ground state of a many-electron system (under the effects of an external potential) is uniquely defined by the ground-state electron density, and (II) The existence of an energy functional of the density $E[n]$ that is minimal for the ground state density $n_{0}(\textbf{r})$ giving the ground state energy.