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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}