deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index ceb7534..69baa13 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
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E=\sum_{i=1}^\infty\int d\mathbf{r} n_{i}\phi^{*}_{i}(\mathbf{r})\left(-\frac{\nabla^2}{2}\right) \phi_{i}(\mathbf{r})+\sum_{i=1}^\infty \int d\mathbf{r} V_{\mathrm{ext}}(\mathbf{r})n_{i}|\phi_{i}(\mathbf{r})|^{2}\nonumber\\  +\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}  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 $\gamma$. A common approximation for $E_{xc}$ is the Mueller, M\"uller,  which has the following form \begin{eqnarray}  E_{xc}(\{n_j\},\{\phi_j\})=\frac{1}{2}\sum_{i,j=1}^\infty 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}  and is the only $E_{xc}$ implemented in octopus for the momment. moment.  \par  For closed-shell systems the necessary and sufficient conditions for the 1-RDM to be $N$-representable, 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.\label{eqsumocc}  \end{eqnarray}  Note that within the RDMFT implementation in octopus only closed-shell systems are treated at the momment. moment.  Minimization of the energy functional of Eq. \ref{eqenergy} 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}. \label{eqorth}  \end{eqnarray}