From 864c6f32f411b7f06f301743abaf6bc527111b02 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Wed, 24 Apr 2019 16:19:38 +0200
Subject: [PATCH] corrections toto

---
 Manuscript/G2-srDFT.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex
index 97c3d5e..81b5f04 100644
--- a/Manuscript/G2-srDFT.tex
+++ b/Manuscript/G2-srDFT.tex
@@ -348,7 +348,7 @@ In order to correct such a defect, we propose here a new Perdew-Burke-Ernzerhof
 	\titou{\beta(\n{}{},s,\zeta) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\text{c}}{\PBE}(\n{}{},s,\zeta)}{\n{2}{\UEG}(0,\n{}{},\zeta)}.}
 \end{gather}
 \end{subequations}
-The difference between the ECMD functional defined in Ref.~\onlinecite{FerGinTou-JCP-18} and the present expression \eqref{eq:epsilon_cmdpbe}-\eqref{eq:beta_cmdpbe} is that we approximate here the on-top pair density by its UEG version, i.e.~\titou{$\n{2}{\Bas}(\br{},\br{})  \approx \n{2}{\UEG}(0,\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(r_{12},\n{}{},\zeta) \approx \n{}{2} (1-\zeta^2) g(r_{12},n)$} with the parametrization of the UEG on-top pair-distribution function $g(0,n)$ given in Eq.~(46) of Ref.~\onlinecite{GorSav-PRA-06}. 
+The difference between the ECMD functional defined in Ref.~\onlinecite{FerGinTou-JCP-18} and the present expression \eqref{eq:epsilon_cmdpbe}-\eqref{eq:beta_cmdpbe} is that we approximate here the on-top pair density by its UEG version, i.e.~\titou{$\n{2}{\Bas}(\br{},\br{})  \approx \n{2}{\UEG}(0,\n{}{}(\br{}),\zeta(\br{}))$, where $\n{2}{\UEG}(r_{12},\n{}{},\zeta) = \n{}{2} (1-\zeta^2) g(r_{12},n)$} with the parametrization of the UEG on-top pair-distribution function $g(0,n)$ given in Eq.~(46) of Ref.~\onlinecite{GorSav-PRA-06}. 
 This represents a major computational saving without loss of accuracy for weakly correlated systems as we eschew the computation of $\n{2}{\Bas}(\br{},\br{})$.
 
 Depending on the functional choice, the complementary functional $\bE{}{\Bas}[\n{\modZ}{\Bas}]$ is approximated by $\bE{\LDA}{\Bas}[\n{\modZ}{\Bas},\rsmu{}{\Bas}]$ or $\bE{\PBE}{\Bas}[\n{\modZ}{\Bas},\rsmu{}{\Bas}]$ where $\rsmu{}{\Bas}(\br{})$ is given by Eq.~\eqref{eq:mu_of_r}.