From 143314894247c219078b223160b32085f8a2610e Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Thu, 14 Nov 2019 22:00:25 +0100
Subject: [PATCH] Cx

---
 Manuscript/FarDFT.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex
index 2667ebe..25e04b7 100644
--- a/Manuscript/FarDFT.tex
+++ b/Manuscript/FarDFT.tex
@@ -224,13 +224,13 @@ with
 
 Knowing that the exchange functional has the following form
 \begin{equation}
-	\e{x}{(I)}(\n{}{}) = \Cx{(I)} \n{}{1/3}
+	\e{x}{(I)}(\n{}{}) = \Cx{(I)} \n{}{1/3},
 \end{equation}
 we obtain
 \begin{align}
-	 \Cx{(0)} & = - \frac{4}{3} \qty( \frac{2}{\pi} )^{1/3},
+	 \Cx{(0)} & = - \frac{4}{3} \qty( \frac{1}{\pi} )^{1/3},
 	 &
-	 \Cx{(1)} & = - \frac{176}{105} \qty( \frac{2}{\pi} )^{1/3}
+	 \Cx{(1)} & = - \frac{176}{105} \qty( \frac{1}{\pi} )^{1/3}
 \end{align}
 We can now combine these two exchange functionals to create a weight-dependent exchange functional
 \begin{equation}
@@ -245,7 +245,7 @@ with
 \begin{equation}
 	\Cx{\ew{}} = (1-\ew{}) \Cx{(0)} + \ew{} \Cx{(1)}
 \end{equation}
-Amazingly, the weight dependence of the exchange functional can be transfered to the Subscript[C, x] coefficient.
+Amazingly, the weight dependence of the exchange functional can be transfered to the $\Cx{}$ coefficient.
 This is obvious but kind of nice.
 
 
@@ -357,7 +357,7 @@ where we use here the Dirac exchange functional and the VWN5 correlation functio
 	\e{c}{\LDA}(\n{}{}) & \equiv \e{c}{\text{VWN5}}(\n{}{}).
 \end{align}
 \end{subequations}
-with $\Cx{\LDA} = -\frac{3}{2} \qty(\frac{3}{4\pi})^{1/3}$.
+with $\Cx{\LDA} = -\frac{3}{4} \qty(\frac{3}{\pi})^{1/3}$.
 
 Equation \eqref{eq:becw} can be recast
 \begin{equation}