deletions | additions       diff --git a/RDMFT.tex b/RDMFT.tex  index afa25bb..494dd02 100644  --- a/RDMFT.tex  +++ b/RDMFT.tex 
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+\frac{1}{2}\sum_{i,j=1}^\infty n_{i} n_{j}\int d\mathbf{r} d\mathbf{r'} \frac{|\phi_{i}(\mathbf{r})|^{2} |\phi_{j}(\mathbf{r})|^{2}}{|\mathbf{r}-\mathbf{r'}|} + E_{xc}\left[\{n_{j}\},\{\phi_{j}\}\right].  \end{eqnarray}  The third term is the Hartree energy, $E_H$ and the forth the exchange-correlation energy $E_{xc}$. As in DFT, the exact functional of RDMFT is unknown. However, the only part that needs to be approximated $E_{xc}[\gamma]$ comes, contrary to DFT, only from the electron-electron interaction, as the interacting kinetic energy can be explicitely expressed in terms of $\gamma$.   Different approximate functionals are employed and minimized with respect to the 1-RDM in order to find the ground state energy, e.g.\ \cite{GPB2005, ML2008, P2013}. \cite{GPB2005,ML2008,P2013}.  A common approximation for $E_{xc}$ is the M\"uller functional \cite{Mueller_1984}, which has the following form \begin{eqnarray}  E_{xc}(\{n_j\},\{\phi_j\})=-\frac{1}{2}\sum_{i,j=1}^\infty \sqrt{n_{i} n_{j}}\int d\mathbf{r} d\mathbf{r'} \frac{\phi_{i}^{*}(\mathbf{r})\phi_i(\mathbf{r'}) \phi_{j}^{*}(\mathbf{r'})\phi_j(\mathbf{r})}{|\mathbf{r}-\mathbf{r'}|}  \end{eqnarray}