H-K theorem I

The Hohenberg-Kohn theorem[11] states that if $N$ interacting electrons move in an external potential $V_{ext}({\bf r})$, the ground-state energy is a unique functional of the density $n({\bf r})$.

Thus the ground state electron density is sufficient to construct the full Hamilton operator and hence to calculate - in principle - any ground state property of the system without the knowledge of the many electron wavefunction. Alternatively formulated, this means that any ground state property can be expressed in terms of the ground state electron density $n({\bf r})$.