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Within Reduced Density Matrix Functional Theory (RDMFT)the total ground state energy is  given as a functional of the one body reduced density matrix (1-RDM) \begin{eqnarray}  \gamma(\mathbf{r},\mathbf{r'})=N\int\cdots\int d\mathbf{r_2}...d\mathbf{r_N} \Psi^*(\mathbf{r'},\mathbf{r_2}...\mathbf{r_N})\Psi(\mathbf{r},\mathbf{r_2}...\mathbf{r_N})  \end{eqnarray}  which can be written in its spectral representation as  \begin{eqnarray}  \gamma(\mathbf{r},\mathbf{r'})=\sum_{i=1}^{\infty}n_{i}\phi^*_i(\mathbf{r'})\phi_i(\mathbf{r}). \gamma(\mathbf{r},\mathbf{r'})=\sum_{i=1}^{\infty}n_{i}\phi^*_i(\mathbf{r'})\phi_i(\mathbf{r}),  \end{eqnarray}  The where the  natural orbitals $\phi_i(\mathbf{r})$ and their occupation numbers $n_i$ are the eigenfunctions and eigenvalues of the 1-RDM, respectively. As in the case of DFT,  the exact functional of RDMFT  is unknown different unknown. Different  approximate functionals are employed and minimized with respect to the 1-RDM in order to find the ground state energy. However, from the total energy \begin{eqnarray}  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}