From 64b9f3ae10e72c6f8c0492d92948269bb603e61c Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Fri, 5 Apr 2019 15:34:11 +0200
Subject: [PATCH] getting there

---
 Manuscript/G2-srDFT.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex
index 0e9fae3..fcb81ac 100644
--- a/Manuscript/G2-srDFT.tex
+++ b/Manuscript/G2-srDFT.tex
@@ -561,14 +561,14 @@ where $\be{\UEG}{\sr}[\n{}{}(\br{}),\rsmu{}{}]$ is the multi-determinant short-r
 %\subsubsection{New PBE functional}
 %--------------------------------------------
 The short-range LDA correlation functional defined in Eq.~\eqref{eq:def_lda_tot} relies on the transferability of the physics of the UEG which is certainly valid for large $\mu$ but is known to over correlate for small $\mu$. 
-In order to correct such a defect, we propose here a new ECMD functional inspired by the recently proposed functional of some of the present authors \cite{FerGinTou-JCP-18} which interpolates between the usual PBE correlation functional $\e{}{\PBE}(\n{}{},\nabla \n{}{})$ for small $\rsmu{}{}$ and the exact large-$\rsmu{}{}$ behaviour, \cite{TouColSav-PRA-04, GoriSav-PRA-06, PazMorGori-PRB-06} yielding
+In order to correct such a defect, we propose here a new ECMD functional inspired by the recently proposed functional of some of the present authors \cite{FerGinTou-JCP-18} which interpolates between the usual PBE correlation functional $\e{\PBE}{}(\n{}{},\nabla \n{}{})$ for small $\rsmu{}{}$ and the exact large-$\rsmu{}{}$ behaviour, \cite{TouColSav-PRA-04, GoriSav-PRA-06, PazMorGori-PRB-06} yielding
 \begin{subequations}
 \begin{gather}
 	\label{eq:epsilon_cmdpbe}
-	\be{\PBE}{\sr}(\n{}{},\nabla \n{}{},\rsmu{}{}) = \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{1 + \beta(n,\nabla n, \mu)\mu^3 }
+	\be{\PBE}{\sr}(\n{}{},\nabla \n{}{},\rsmu{}{}) = \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{1 + \beta(n,\nabla n, \rsmu{}{})\rsmu{}{3} }
 	\\
 	\label{eq:epsilon_cmdpbe}
-	\beta(n,\nabla n;\,\mu) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{\n{\UEG}{(2)}(\n{}{})}.
+	\beta(n,\nabla n,\rsmu{}{}) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{\n{\UEG}{(2)}(\n{}{})}.
 \end{gather}
 \end{subequations}
 The difference between the ECMD PBE functional defined in Ref.~\cite{FerGinTou-JCP-18} and the present expression is that we approximate the \textit{exact} ground-state on-top pair density of the system $\n{}{(2)}(\br{})$ by its UEG version, i.e.