deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index 9259169..feb3d92 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
...
% \sum_i \int d\mathbf{r} \delta \phi_i(\mathbf{r})\Big[\frac{\delta E}{\delta \phi_{i}(\mathbf{r})}-\sum_{k}\lambda_{ki}\phi_{k}^{*}(\mathbf{r})\Big] = 0  %\end{eqnarray}  In practice, the minimization of the energy is not performed with respect to the 1-RDM but with respect to $n_{i}$ and $\phi_{i}$, separately. Thus, for a fixed set of orbitals the energy functional is minimized with respect to occupation numbers and accordingly for a fixed set of occupations the energy functional is minimized with respect to variations of the orbitals until overall convergence is achieved. For the first step of occupation numbers minimization HF orbitals are used. As the correct $\mu$ is not known bisection is used. For every $\mu$, the objective functional is minimized with respect to $\vartheta_i$ until the condition \ref{eqsumocc}\par \ref{eqsumocc} is satisfied.\par  The implementation of the natural orbital minimization follows a method by Piris and Ugalde (\cite{Piris}). As one can show for fixed occupation numbers  \begin{eqnarray}  \lambda_{ki}=h_{ki}n_i+\int d\mathbf{r} \frac{\delta V_{ee}}{\delta \phi_i^{*}(\mathbf{r})}\phi_k^{*}(\mathbf{r}).