\subsubsection{Hohenberg-Kohn theorem}
-Considering a system with a nondegenerate ground state, there is obviously only one ground-state charge density $n_0(\vec{r})$ that correpsonds to a given potential $V(\vec{r})$.
+Considering a system with a nondegenerate ground state, there is obviously only one ground-state charge density $n_0(\vec{r})$ that corresponds to a given potential $V(\vec{r})$.
In 1964, Hohenberg and Kohn showed the opposite and far less obvious result \cite{hohenberg64}.
For a nondegenerate ground state, the ground-state charge density uniquely determines the external potential in which the electrons reside.
The proof presented by Hohenberg and Kohn proceeds by {\em reductio ad absurdum}.
\int n(\vec{r}) \left( V_2(\vec{r})-V_1(\vec{r}) \right) d\vec{r}
}_{=0}
\end{equation}
-is revealed.
+is revealed, which proofs the Hohenberg Kohn theorem.