Density functional theory/Hohenberg–Kohn theorems

Hohenberg–Kohn theoremsEdit

1. If two systems of electrons, one trapped in a potential   and the other in  , have the same ground-state density   then necessarily  .

Corollary: the ground state density uniquely determines the potential and thus all properties of the system, including the many-body wave function. In particular, the "HK" functional, defined as   is a universal functional of the density (not depending explicitly on the external potential).

2. For any positive integer   and potential   it exists a density functional   such that   obtains its minimal value at the ground-state density of   electrons in the potential  . The minimal value of   is then the ground state energy of this system.