From 7d9d9f86cf2596b339b8c8556caed5360a060463 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Fri, 12 Apr 2019 14:12:02 +0200
Subject: [PATCH] RSDFT

---
 Manuscript/G2-srDFT.tex | 21 +++++++++++++++++----
 1 file changed, 17 insertions(+), 4 deletions(-)

diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex
index 0e6e2d9..6859815 100644
--- a/Manuscript/G2-srDFT.tex
+++ b/Manuscript/G2-srDFT.tex
@@ -310,16 +310,29 @@ Once defined, $\rsmu{\Bas}{}(\br{})$ can be used in RS-DFT functionals to approx
 As in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, we consider here a specific class of short-range correlation functionals known as ECMD whose general definition reads \cite{TouGorSav-TCA-05}
 \begin{multline}
   \label{eq:ec_md_mu}
-  \bE{}{\sr}[\n{}{}(\br{}),\rsmu{}{}] = \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\Psi}{\hT + \hWee{}}{\wf{}{}}
+  \bE{}{\sr}[\n{}{}(\br{}),\rsmu{}{}] 
+  = \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\Psi}{\hT + \hWee{}}{\wf{}{}}
   \\
-  - \mel*{\wf{}{\rsmu{}{}}[\n{}{}(\br{})]}{\hT + \hWee{}}{\wf{}{\rsmu{}{}}[\n{}{}(\br{})]},
+  - \mel*{\wf{}{\rsmu{}{}}}{\hT + \hWee{}}{\wf{}{\rsmu{}{}}},
 \end{multline}
-where $\wf{}{\rsmu{}{}}[\n{}{}(\br{})]$ is defined by the constrained minimization
+where $\wf{}{\rsmu{}{}}$ is defined by the constrained minimization
 \begin{equation}
 \label{eq:argmin}
-	\wf{}{\rsmu{}{}}[\n{}{}(\br{})] = \arg \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\wf{}{}}{\hT + \hWee{\lr,\rsmu{}{}}}{\wf{}{}},
+	\wf{}{\rsmu{}{}} = \arg \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\wf{}{}}{\hT + \hWee{\lr,\rsmu{}{}}}{\wf{}{}},
 \end{equation}
 with $\hWee{\lr,\rsmu{}{}} = \sum_{i<j} \w{}{\lr,\rsmu{}{}}(r_{ij})$.
+%\begin{multline}
+%  \label{eq:ec_md_mu}
+%  \bE{}{\sr}[\n{}{}(\br{}),\rsmu{}{}] = \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\Psi}{\hT + \hWee{}}{\wf{}{}}
+%  \\
+%  - \mel*{\wf{}{\rsmu{}{}}[\n{}{}(\br{})]}{\hT + \hWee{}}{\wf{}{\rsmu{}{}}[\n{}{}(\br{})]},
+%\end{multline}
+%where $\wf{}{\rsmu{}{}}[\n{}{}(\br{})]$ is defined by the constrained minimization
+%\begin{equation}
+%\label{eq:argmin}
+%	\wf{}{\rsmu{}{}}[\n{}{}(\br{})] = \arg \min_{\wf{}{} \to \n{}{}(\br{})} \mel*{\wf{}{}}{\hT + \hWee{\lr,\rsmu{}{}}}{\wf{}{}},
+%\end{equation}
+%with $\hWee{\lr,\rsmu{}{}} = \sum_{i<j} \w{}{\lr,\rsmu{}{}}(r_{ij})$.
 %and
 %\begin{equation}
 %\label{eq:erf}