deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index b39723d..5c82f74 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
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F_{ki}=\theta(i-k)(\lambda_{ki}-\lambda^{*}_{ik})+\theta(k-i)(\lambda^{*}_{ik}-\lambda_{ki})\label{eqF}  \end{eqnarray}  where $\theta$ is the unit-step Heavside function. This matrix is diagonal at the extremum and hence the matrix $\mathbf{F}$ and $\gamma$ can be brought simultaneously to a diagonal form at the solution. Thus, the $\{\phi_i\}$ which are the solutions of Eq. (\ref{eqlambda}) can be found by diagonalization of $\mathbf{F}$ in an iterative manner. As the matrix $\mathbf{F}$, as defined in \ref{eqF} is zero in the diagonal, in every step the diagonal of the previous step is used and for the first step the matrix $(\lambda_{ki}+\lambda_{ik}^{*})/2$ is diagonalized (see \cite{Piris} for details).\par  One needs an initial guess of the natural orbitals both for the first step of occupation number optimization and for the natural orbitals one. A first rather obvious choice for that would be to run a DFT or HF calculation using unoccupied states with octopus and getting the output states as inital guess for the natural orbitals in a RDMFT calculation. Unfortunatelly, as we found out there are unbound states among the HF (or DFT) unoccupied states which are bad starting point for the weakly occupied natural orbitals. This is not surprising as especially the higher unoccupied HF or DFT orbitals see in practice no potential so they act like particles in a box. When we used HF or DFT orbitals to start a RDMFT calculation, the natural orbitals did not converge to any reasonable shape (some of the weakly occupied natural orbitals were still unbound). We tried to get some more localized states as initial guess by performing a HF or DFT plus smearing calculation with some artifical smearing but this choice did not work either. In order to check that the only problem of the RDMFT implementation in octopus is the appropriate choice of an initial guess, we performed in our private version of the code RDMFT calculations using as initial guess for the natural orbitals HF orbitals from a gaussian basis code which are more localized due to the fact that they have to be linear combination of gaussians. With this initial guess we found natural orbitals that looked reasonable. In the plot we give a RDMFT Energy curve of H$_2$ versus internuclear distance and we see that this curve looks the same way as in other implementations of RDMFT (cite..) keeping the nice feature of not diverging in the dissociation limit. However, we have not yet found a way to have a good initial guess within octopus and that's something we are working on at the moment. The treatment of open-shell systems within RDMFT and the inclusion of other $E_xc$ functionals apart from M\"uller are things we would like to implement in the near future.