Nicole Helbig edited RDMFT1.tex  over 9 years ago

Commit id: 5db99ba2d1b1038a028e583786f1f36fa25d462f

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\end{eqnarray}  and is the only $E_{xc}$ implemented in octopus for the moment.   \par  For closed-shell systems the necessary and sufficient conditions for the 1-RDM to be $N$-representable, $N$-representable \cite{Coleman_1963},  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 moment. Minimization of the energy functional of Eq. \ref{eqenergy} (\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}