deletions | additions       diff --git a/RDMFT1.tex b/RDMFT1.tex  index a95f7e4..d2c24ab 100644  --- a/RDMFT1.tex  +++ b/RDMFT1.tex 
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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). (1-RDM)  \begin{eqnarray}  \gamma(x,x')=\sum_{i=1}^{\infty}n_{i}\phi^{*}(x')\phi(x). \gamma(x,x')=N\int\cdots\int dx_2...dx_N \Psi^*(x',x_2...x_N)\Psi(x,x_2...x_N)  \end{eqnarray}  which can be written in its spectral representation as  \begin{eqnarray}  \gamma(x,x')=\sum_{i=1}^{\infty}n_{i}\phi^*_i(x')\phi_i(x).  \end{eqnarray}  The natural orbitals $\phi_i(x)$ and their occupation numbers $n_i$ are the eigenfunctions and eigenvalues of the 1-RDM, respectively.  As the exact functional is unknown different approximate functionals are employed and minimized with respect to the 1-RDM in order to find the ground state energy. However, the part that needs to be approximated $E_{xc}(\gamma)$ comes only from the interaction term (contrary to KS-DFT), as the kinetic energy can be explicitely expressed with respect to $\gamma$. In practice, the minimization of the energy is not performed with respect to the 1-RDM ($\gamma$) but with respect to its eigenvalues which are named occupation numbers n$_{i}$ $n_{i}$  andeigenfunctions, the natural orbitals  $\phi_{i}$, separately. \begin{eqnarray}  E=-\frac{1}{2}\int dx\sum n_{i}\phi^{*}_{i}(x)\nabla^{2} \phi_{i}(x)+\int dx V_{ext}(x)\sum n_{i}|\phi_{i}(x)|^{2}+\nonumber\\  \frac{\int dx dx' \sum_{i} n_{i}|\phi_{i}(x)|^{2}\sum_{j} n_{j} |\phi_{j}(x)|^{2}}{2|x-x'|} + E_{xc}(\{n_{j}\},\{\phi_{j}\})