deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index 5c82f74..f0978e2 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
...
Within Reduced Density Matrix Functional Theory (RDMFT) \cite{Gilbert}  the total energy of a system is given as a functional of the one body reduced density matrix (1-RDM) \begin{eqnarray}  \gamma(\mathbf{r},\mathbf{r'})=N\int\cdots\int d\mathbf{r_2}...d\mathbf{r_N} \Psi^*(\mathbf{r'},\mathbf{r_2}...\mathbf{r_N})\Psi(\mathbf{r},\mathbf{r_2}...\mathbf{r_N})  \end{eqnarray} 
...
+\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].\label{eqenergy}  \end{eqnarray}  As in the case of DFT, the exact functional of RDMFT is unknown. The part that needs to be approximated $E_{xc}[\gamma]$ comes only from the interaction term (contrary to KS-DFT), 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. A common approximation for $E_{xc}$ is the M\"uller functional, functional \cite{Mueller},  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}