deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index ee44f06..dbc1491 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.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]\label{eqn:energy}  \end{eqnarray}  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 $\gamma$.  For closed-shell systems the necessary and sufficient conditions for the 1-RDM to be $N$-representable, i.e.\ i.e.  to correspond to a $N$-electron wavefunction is that $ 0 \leq n_{i} \leq 2$ and \begin{eqnarray}  \sum_{i=1}^{\infty}n_{i}=N.  \end{eqnarray}  Note that within the RDMFT implementation in octopus only closed-shell systems are treated at the momment. Minimization of the energy functional of Eq. ref{eqn:energy} (\ref{eqn:energy})  is performed under the $N$-representability constraints and the orthonormality requierements of the natural orbitals, \begin{eqnarray}  \langle \phi_{i} | \phi_{j}\rangle = \delta_{ij}  \end{eqnarray}