From 040760906884ee9777afb3836c9767a0c1573aa1 Mon Sep 17 00:00:00 2001
From: Pierre-Francois Loos <pierrefrancois.loos@gmail.com>
Date: Tue, 23 Apr 2019 15:11:48 +0200
Subject: [PATCH] minor

---
 Manuscript/G2-srDFT.tex | 2 --
 1 file changed, 2 deletions(-)

diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex
index fcc157f..825836c 100644
--- a/Manuscript/G2-srDFT.tex
+++ b/Manuscript/G2-srDFT.tex
@@ -209,7 +209,6 @@ where
 is the basis-dependent complementary density functional, $\hT$ is the kinetic operator and $\hWee{} = \sum_{i<j} r_{ij}^{-1}$ is the interelectronic repulsion operator.
 In Eq.~\eqref{eq:E_funcbasis}, $\wf{}{\Bas}$ and $\wf{}{}$ are two general $\Ne$-electron normalized wave functions belonging to the Hilbert space spanned by $\Bas$ and the complete basis set (CBS), respectively.
 Both wave functions yield the same target density $\n{}{}$ (assumed to be representable in \trashPFL{the basis set} $\Bas$). 
-
 Importantly, in the CBS limit (which we refer to as $\Bas \to \infty$), we have, for any density $\n{}{}$, $\lim_{\Bas \to \infty} \bE{}{\Bas}[\n{}{}] = 0$. 
 This implies that
 \begin{equation}
@@ -270,7 +269,6 @@ Because Eq.~\eqref{eq:int_eq_wee} can be \titou{recast} as
 \end{equation}
 it intuitively motivates $\W{}{\Bas}(\br{1},\br{2})$ as a potential candidate for an effective interaction.
 Note that the divergence condition of $\W{}{\Bas}(\br{1},\br{2})$ in Eq.~\eqref{eq:def_weebasis} ensures that one-electron systems are free of correction as the present approach must only correct the basis set incompleteness error originating from the e-e cusp.
-
 As already discussed in Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, $\W{}{\Bas}(\br{1},\br{2})$ is symmetric, \textit{a priori} non translational, nor rotational invariant if $\Bas$ does not have such symmetries. 
 Thanks to its definition one can show that (see Appendix B of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}) 
 \begin{equation}