diff --git a/Manuscript/C2_CVXZ.pdf b/Manuscript/C2_CVXZ.pdf
deleted file mode 100644
index 0bd9939..0000000
Binary files a/Manuscript/C2_CVXZ.pdf and /dev/null differ
diff --git a/Manuscript/G2-srDFT.tex b/Manuscript/G2-srDFT.tex
index 750307d..f34b561 100644
--- a/Manuscript/G2-srDFT.tex
+++ b/Manuscript/G2-srDFT.tex
@@ -89,7 +89,7 @@
 
 % basis sets 
 \newcommand{\Bas}{\mathcal{B}}
-\newcommand{\BasFC}{\Bar{\mathcal{B}}}
+\newcommand{\BasFC}{\mathcal{A}}
 \newcommand{\FC}{\text{FC}}
 \newcommand{\occ}{\text{occ}}
 \newcommand{\virt}{\text{virt}}
@@ -119,6 +119,9 @@
 
 \title{A Density-Based Basis Set Correction For Wave Function Theory}
 
+\author{Pierre-Fran\c{c}ois Loos}
+\email{loos@irsamc.ups-tlse.fr}
+\affiliation{\LCPQ}
 \author{Bath\'elemy Pradines}
 \affiliation{\LCT}
 \affiliation{\ISCD}
@@ -127,9 +130,6 @@
 \author{Julien Toulouse}
 \email{toulouse@lct.jussieu.fr}
 \affiliation{\LCT}
-\author{Pierre-Fran\c{c}ois Loos}
-\email{loos@irsamc.ups-tlse.fr}
-\affiliation{\LCPQ}
 \author{Emmanuel Giner}
 \email{emmanuel.giner@lct.jussieu.fr}
 \affiliation{\LCT}
@@ -205,7 +205,7 @@ Importantly, in the limit of a complete basis set (which we refer to as $\Bas \t
         \lim_{\Bas \to \infty} \qty( \E{\modY}{\Bas} + \bE{}{\Bas}[\n{\modZ}{\Bas}] ) = \E{\modY}{} \approx E,
 \end{equation}
 where  $\E{\modY}{}$ is the energy associated with the method $\modY$ in the complete basis set.
-In the case $\modY = \FCI$ \manu{in \eqref{eq:limitfunc}}, we have a strict equality as $\E{\FCI}{} = \E{}{}$.
+In the case where $\modY = \FCI$ in Eq.~\eqref{eq:limitfunc}, we have a strict equality as $\E{\FCI}{} = \E{}{}$.
 Provided that the functional $\bE{}{\Bas}[\n{}{}]$ is known exactly, the only source of error at this stage lies in the potential approximate nature of the methods $\modY$ and $\modZ$.% for the FCI energy and density within $\Bas$, respectively.
 
 The functional $\bE{}{\Bas}[\n{}{}]$ is obviously \textit{not} universal as it depends on $\Bas$. 
@@ -239,7 +239,7 @@ where
 	\n{2}{}(\br{1},\br{2})
 	= \sum_{pqrs \in \Bas}  \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
 \end{equation}
-and $\Gam{pq}{rs} = \manu{1/2\mel*{\wf{}{\Bas}}{ \aic{r\downarrow}\aic{s\uparrow}\ai{p\uparrow}\ai{q\downarrow} + \aic{r\uparrow}\aic{s\downarrow}\ai{p\downarrow}\ai{q\uparrow} }{\wf{}{\Bas}}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor (respectively), $\SO{p}{}$ is a \trashMG{spinorbital}\manu{spatial orbital},
+and $\Gam{pq}{rs} =\mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{p_\uparrow}\ai{q_\downarrow}}{\wf{}{\Bas}}$ are the opposite-spin pair density associated with $\wf{}{\Bas}$ and its corresponding tensor (respectively), $\SO{p}{}$ is a molecular orbital (MO),
 \begin{equation}
 	\label{eq:fbasis}
 	\f{\Bas}{}(\br{1},\br{2}) 
@@ -377,8 +377,8 @@ Depending on the functional choice, the complementary functional $\bE{}{\Bas}[\n
 %\subsection{Valence approximation}
 %=================================================================
 
-As most WFT calculations are performed within the frozen-core (FC) approximation, it is important to define an effective interaction within a subset of spinorbitals. 
-We then naturally split the basis set as $\Bas = \Cor \bigcup \BasFC$, where $\Cor$ is the set of core \trashMG{spinorbitals} \manu{spatial orbitals}, and define the FC version of the effective interaction as
+As most WFT calculations are performed within the frozen-core (FC) approximation, it is important to define an effective interaction within a subset of MOs. 
+We then naturally split the basis set as $\Bas = \Cor \bigcup \BasFC$, where $\Cor$ is the set of core MOs, and define the FC version of the effective interaction as
  \begin{equation}
 	\W{\Bas}{\FC}(\br{1},\br{2})  = 
     \begin{cases}
@@ -488,7 +488,6 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
 \end{figure*}
 
 We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5).
-\titou{In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.}
 \ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} 
 In a second time, we compute the atomization energies of the entire G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of basis sets.
 This molecular set has been exhausively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08, Gro-JCP-09, FelPet-JCP-09, NemTowNee-JCP-10, FelPetHil-JCP-11, HauKlo-JCP-12, PetTouUmr-JCP-12, FelPet-JCP-13, KesSylKohTewMar-JCP-18}) \titou{and can be considered as a representative set for typical quantum chemical calculations on small organic molecules}.
@@ -503,7 +502,7 @@ RS-DFT and exFCI calculations are performed with {\QP}. \cite{QP2}
 For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
 Except for the carbon dimer where we have taken the experimental equilibrium bond length (\InAA{1.2425}), all geometries have been extracted from Ref.~\onlinecite{HauJanScu-JCP-09} and have been obtained at the B3LYP/6-31G(2df,p) level of theory.
 Frozen-core calculations are defined as such: an \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
-In the context of the basis set correction, the set of spinorbitals $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
+In the context of the basis set correction, the set of MOs $\BasFC$ involved in the definition of the effective interaction refers to the non-frozen MOs.
 The FC density-based correction is set consistently when the FC approximation was applied in WFT methods.
 In order to estimate the complete basis set (CBS) limit for each model, \manu{following the work of Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98}}, 
 we employ the two-point extrapolation for the correlation energies \manu{for each model in quadruple- and quintuple-$\zeta$ basis sets, which is refered to as $\CBS$ correlation energies, and we add the HF energies in the largest basis sets (\textit{i.e.} quintuple-$\zeta$ quality basis sets) to the CBS correlation energies to estimate the CBS FCI energies.}
diff --git a/Manuscript/N2_CVXZ.pdf b/Manuscript/N2_CVXZ.pdf
deleted file mode 100644
index c2f5afe..0000000
Binary files a/Manuscript/N2_CVXZ.pdf and /dev/null differ
diff --git a/Manuscript/SI/G2_srDFT-SI.tex b/Manuscript/SI/G2_srDFT-SI.tex
index 47028a1..a0630b6 100644
--- a/Manuscript/SI/G2_srDFT-SI.tex
+++ b/Manuscript/SI/G2_srDFT-SI.tex
@@ -118,16 +118,18 @@
 
 \title{Supplementary Information for ``A Density-Based Basis Set Correction For Wave Function Theory''}
 
+\author{Pierre-Fran\c{c}ois Loos}
+\email{loos@irsamc.ups-tlse.fr}
+\affiliation{\LCPQ}
 \author{Bath\'elemy Pradines}
 \affiliation{\LCPQ}
 \author{Anthony Scemama}
 \affiliation{\LCPQ}
 \author{Julien Toulouse}
+\email{toulouse@lct.jussieu.fr}
 \affiliation{\LCT}
-\author{Pierre-Fran\c{c}ois Loos}
-\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
-\affiliation{\LCPQ}
 \author{Emmanuel Giner}
+\email{emmanuel.giner@lct.jussieu.fr}
 \affiliation{\LCT}
 
 \begin{abstract}
@@ -139,51 +141,51 @@
 \begin{table*}
 	\caption{
 		\label{tab:diatomics}
-		Atomization energies (in {\kcal}) of \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} computed with various methods and basis sets.
+		Frozen-core atomization energies (in {\kcal}) of \ce{C2}, \ce{O2}, \ce{N2} and \ce{F2} computed with various methods and basis sets.
 		The deviations with respect to the corresponding CBS values are reported in parenthesis.
 		}
 		\begin{ruledtabular}
 			\begin{tabular}{llddddd}
-							&					&	\mc{4}{c}{Dunning's basis set}													
+							&					&	\mc{4}{c}{Dunning's basis set cc-pVXZ}													
 				\\
 													\cline{3-6}
                   Molecule	&	Method				&	\tabc{$\X = \D$}	&	\tabc{$\X = \T$}	&	\tabc{$\X = \Q$}	&	\tabc{$\X = 5$}		&	\tabc{CBS}	
 				\\
 				\hline
-				\ce{C2}		&	exFCI\fnm[1]		&	132.0	(-13.7	)	&	140.3	(-5.4	)	&	143.6	(-2.1	)	&	144.7	(-1.0	)	&	145.7			\\	
-				(cc-pVXZ)	&	exFCI+LDA\fnm[1]	&	141.3	(-4.4	)	&	145.1	(-0.6	)	&	146.4	(+0.7	)	&	146.3	(+0.6	)	&					\\	
-							&	exFCI+PBE\fnm[1]	&	145.7	(+0.0	)	&	145.7	(+0.0	)	&	146.3	(+0.6	)	&	146.2	(+0.5	)	&					\\	
-                            &	CCSD(T)\fnm[1]		&	129.2	(-16.2	)	&	139.1	(-6.3	)	&	143.0	(-2.4	)	&	144.2	(-1.2	)	&   145.4		\\
-							&	CCSD(T)+LDA\fnm[1]	&	139.1	(-6.3	)	&	143.7	(-1.7	)	&	145.9	(+0.5	)	&	145.9	(+0.5	)	&					\\	
-							&	CCSD(T)+PBE\fnm[1]	&	142.8	(-2.6	)	&	144.2	(-1.2	)	&	145.9	(+0.5	)	&	145.8	(+0.4	)	&				\\	\\
-				\ce{C2}	   	&	exFCI\fnm[2]		&	131.0	(-16.1	)	&	141.5	(-5.6	)	&	145.1	(-2.0	)	&	146.1	(-1.0	)	&	147.1			\\	
-				(cc-pCVXZ)	&	exFCI+LDA\fnm[2]	&	141.4	(-5.7	)	&	146.7	(-0.4	)	&	147.8	(+0.7	)	&	147.6	(+0.5	)	&					\\	
-							&	exFCI+PBE\fnm[2]	&	145.1	(-2.0	)	&	147.0	(-0.1	)	&	147.7	(+0.6	)	&	147.5	(+0.4	)	&				\\	\\
-				\ce{N2}		&	exFCI\fnm[1]		&	201.1	(-26.7	)	&	217.1	(-10.7	)	&	223.5	(-4.3	)	&	225.7	(-2.1	)	&	227.8       	\\
-				(cc-pVXZ)	&	exFCI+LDA\fnm[1]	&	217.9	(-9.9	)	&	225.9	(-1.9	)	&	228.0	(+0.2	)	&	228.6	(+0.8	)	&					\\	
-							&	exFCI+PBE\fnm[1]	&	227.7	(-0.1	)	&	227.8	(+0.0	)	&	228.3	(+0.5	)	&	228.5	(+0.7	)	&					\\	
-                            &	CCSD(T)\fnm[1]		&	199.9	(-27.3	)	&	216.3	(-10.9	)	&	222.8	(-4.4	)	&	225.0	(-2.2	)	&	227.2			\\
-							&	CCSD(T)+LDA\fnm[1]	&	216.3	(-10.9	)	&	224.8	(-2.4	)	&	227.2	(-0.0	)	&	227.8	(+0.6	)	&					\\	
-							&	CCSD(T)+PBE\fnm[1]	&	225.9	(-1.3	)	&	226.7	(-0.5	)	&	227.5	(+0.3	)	&	227.8	(+0.6	)	&				\\	\\
-				\ce{N2}		&	exFCI\fnm[2]		&	202.2	(-26.6	)	&	218.5	(-10.3	)	&	224.4	(-4.4	)	&	226.6 	(-2.2	)	&	 228.8			\\
-				(cc-pCVXZ)	&	exFCI+LDA\fnm[2]	&	218.0	(-10.8	)	&	226.8	(-2.0	)	&	229.1	(+0.3	)	&	229.4	(+0.6	)	&					\\
-							&	exFCI+PBE\fnm[2]	&	226.4	(-2.4	)	&	228.2	(-0.6	)	&	229.1	(+0.3	)	&	229.2	(+0.4	)	&				\\	\\
-				\ce{O2}		&	exFCI\fnm[1]		&	105.2	(-14.8	)	&	114.5	(-5.5	)	&	118.0	(-2.0	)	&	119.1	(-0.9	)	&	120.0       	\\
-				(cc-pVXZ)	&	exFCI+LDA\fnm[1]	&	112.4	(-7.6	)	&	118.4	(-1.6	)	&	120.2	(+0.2	)	&	120.4	(+0.4	)	&					\\	
-							&	exFCI+PBE\fnm[1]	&	117.2	(-2.8	)	&	119.4	(-0.6	)	&	120.3	(+0.3	)	&	120.4	(+0.4	)	&					\\	
-                            &	CCSD(T)\fnm[1]		&	103.9	(-16.1	)	&	113.6	(-6.0	)	&	117.1	(-2.5	)	&	118.6	(-1.0	)	&	119.6			\\
-							&	CCSD(T)+LDA\fnm[1]	&	110.6	(-9.0	)	&	117.2	(-2.4	)	&	119.2	(-0.4	)	&	119.8	(+0.2	)	&					\\	
-							&	CCSD(T)+PBE\fnm[1]	&	115.1	(-4.5	)	&	118.0	(-1.6	)	&	119.3	(-0.3	)	&	119.8	(+0.2	)	&				\\	\\
-				\ce{F2}		&	exFCI\fnm[1]		&	26.7	(-12.3	)	&	35.1	(-3.9	)	&	37.1	(-1.9	)	&	38.0	(-1.0	)	&	39.0			\\
-				(cc-pVXZ)	&	exFCI+LDA\fnm[1]	&	30.4	(-8.6	)	&	37.2	(-1.8	)	&	38.4	(-0.6	)	&	38.9	(-0.1	)	&					\\	
-							&	exFCI+PBE\fnm[1]	&	33.1	(-5.9	)	&	37.9	(-1.1	)	&	38.5	(-0.5	)	&	38.9	(-0.1	)	&					\\	
-                            &	CCSD(T)\fnm[1]		&	25.7 	(-12.5	)	&	34.4 	(-3.8	)	&	36.5 	(-1.7	)	&	37.4 	(-0.8	)	&	38.2 			\\
-							&	CCSD(T)+LDA\fnm[1]	&	29.2 	(-9.0	)	&	36.5 	(-1.7	)	&	37.2 	(-1.0	)	&	38.2 	(+0.0	)	&					\\	
-							&	CCSD(T)+PBE\fnm[1]	&	31.5 	(-6.7	)	&	37.1 	(-1.1	)	&	37.8 	(-0.4	)	&	38.2 	(+0.0	)	&					\\	
+				\ce{C2}		&	exFCI		&	132.0	(-13.7	)	&	140.3	(-5.4	)	&	143.6	(-2.1	)	&	144.7	(-1.0	)	&	145.7			\\	
+							&	exFCI+LDA	&	141.3	(-4.4	)	&	145.1	(-0.6	)	&	146.4	(+0.7	)	&	146.3	(+0.6	)	&					\\	
+							&	exFCI+PBE	&	145.7	(+0.0	)	&	145.7	(+0.0	)	&	146.3	(+0.6	)	&	146.2	(+0.5	)	&					\\	
+                            &	CCSD(T)		&	129.2	(-16.2	)	&	139.1	(-6.3	)	&	143.0	(-2.4	)	&	144.2	(-1.2	)	&   145.4		\\
+							&	CCSD(T)+LDA	&	139.1	(-6.3	)	&	143.7	(-1.7	)	&	145.9	(+0.5	)	&	145.9	(+0.5	)	&					\\	
+							&	CCSD(T)+PBE	&	142.8	(-2.6	)	&	144.2	(-1.2	)	&	145.9	(+0.5	)	&	145.8	(+0.4	)	&				\\	\\
+%				\ce{C2}	   	&	exFCI\fnm[2]		&	131.0	(-16.1	)	&	141.5	(-5.6	)	&	145.1	(-2.0	)	&	146.1	(-1.0	)	&	147.1			\\	
+%				(cc-pCVXZ)	&	exFCI+LDA\fnm[2]	&	141.4	(-5.7	)	&	146.7	(-0.4	)	&	147.8	(+0.7	)	&	147.6	(+0.5	)	&					\\	
+%							&	exFCI+PBE\fnm[2]	&	145.1	(-2.0	)	&	147.0	(-0.1	)	&	147.7	(+0.6	)	&	147.5	(+0.4	)	&				\\	\\
+				\ce{N2}		&	exFCI		&	201.1	(-26.7	)	&	217.1	(-10.7	)	&	223.5	(-4.3	)	&	225.7	(-2.1	)	&	227.8       	\\
+							&	exFCI+LDA	&	217.9	(-9.9	)	&	225.9	(-1.9	)	&	228.0	(+0.2	)	&	228.6	(+0.8	)	&					\\	
+							&	exFCI+PBE	&	227.7	(-0.1	)	&	227.8	(+0.0	)	&	228.3	(+0.5	)	&	228.5	(+0.7	)	&					\\	
+                            &	CCSD(T)		&	199.9	(-27.3	)	&	216.3	(-10.9	)	&	222.8	(-4.4	)	&	225.0	(-2.2	)	&	227.2			\\
+							&	CCSD(T)+LDA	&	216.3	(-10.9	)	&	224.8	(-2.4	)	&	227.2	(-0.0	)	&	227.8	(+0.6	)	&					\\	
+							&	CCSD(T)+PBE	&	225.9	(-1.3	)	&	226.7	(-0.5	)	&	227.5	(+0.3	)	&	227.8	(+0.6	)	&				\\	\\
+%				\ce{N2}		&	exFCI\fnm[2]		&	202.2	(-26.6	)	&	218.5	(-10.3	)	&	224.4	(-4.4	)	&	226.6 	(-2.2	)	&	 228.8			\\
+%				(cc-pCVXZ)	&	exFCI+LDA\fnm[2]	&	218.0	(-10.8	)	&	226.8	(-2.0	)	&	229.1	(+0.3	)	&	229.4	(+0.6	)	&					\\
+%							&	exFCI+PBE\fnm[2]	&	226.4	(-2.4	)	&	228.2	(-0.6	)	&	229.1	(+0.3	)	&	229.2	(+0.4	)	&				\\	\\
+				\ce{O2}		&	exFCI		&	105.2	(-14.8	)	&	114.5	(-5.5	)	&	118.0	(-2.0	)	&	119.1	(-0.9	)	&	120.0       	\\
+							&	exFCI+LDA	&	112.4	(-7.6	)	&	118.4	(-1.6	)	&	120.2	(+0.2	)	&	120.4	(+0.4	)	&					\\	
+							&	exFCI+PBE	&	117.2	(-2.8	)	&	119.4	(-0.6	)	&	120.3	(+0.3	)	&	120.4	(+0.4	)	&					\\	
+                            &	CCSD(T)		&	103.9	(-16.1	)	&	113.6	(-6.0	)	&	117.1	(-2.5	)	&	118.6	(-1.0	)	&	119.6			\\
+							&	CCSD(T)+LDA	&	110.6	(-9.0	)	&	117.2	(-2.4	)	&	119.2	(-0.4	)	&	119.8	(+0.2	)	&					\\	
+							&	CCSD(T)+PBE	&	115.1	(-4.5	)	&	118.0	(-1.6	)	&	119.3	(-0.3	)	&	119.8	(+0.2	)	&				\\	\\
+				\ce{F2}		&	exFCI		&	26.7	(-12.3	)	&	35.1	(-3.9	)	&	37.1	(-1.9	)	&	38.0	(-1.0	)	&	39.0			\\
+							&	exFCI+LDA	&	30.4	(-8.6	)	&	37.2	(-1.8	)	&	38.4	(-0.6	)	&	38.9	(-0.1	)	&					\\	
+							&	exFCI+PBE	&	33.1	(-5.9	)	&	37.9	(-1.1	)	&	38.5	(-0.5	)	&	38.9	(-0.1	)	&					\\	
+                            &	CCSD(T)		&	25.7 	(-12.5	)	&	34.4 	(-3.8	)	&	36.5 	(-1.7	)	&	37.4 	(-0.8	)	&	38.2 			\\
+							&	CCSD(T)+LDA	&	29.2 	(-9.0	)	&	36.5 	(-1.7	)	&	37.2 	(-1.0	)	&	38.2 	(+0.0	)	&					\\	
+							&	CCSD(T)+PBE	&	31.5 	(-6.7	)	&	37.1 	(-1.1	)	&	37.8 	(-0.4	)	&	38.2 	(+0.0	)	&					\\	
 		\end{tabular}
 	\end{ruledtabular}
-	\fnt[1]{Frozen core calculations. Only valence spinorbitals are taken into account in the basis set correction.}
-	\fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.}
+%	\fnt[1]{ calculations. Only valence orbitals are taken into account in the basis set correction.}
+%	\fnt[2]{``Full'' calculation, i.e., all electrons are correlated. All spinorbitals are taken into account in the basis set correction.}
 \end{table*}
 
 
@@ -192,11 +194,11 @@
 \begin{table}
 	\caption{
 	\label{tab:AE}
-	Deviation from the reference CBS correlation energies (in {\kcal}) for various methods and basis sets.}
+	Deviation from the reference CBS atomization energies (in {\kcal}) for various methods and basis sets.}
 		\begin{ruledtabular}
 			\begin{tabular}{lddddddddddd}
 							&	
-							&	\mc{10}{c}{Deviation from CBS correlation energies}	\\ 
+							&	\mc{10}{c}{Deviation from CBS atomization energies}	\\ 
 							\cline{3-12}
 							&		&	\mc{4}{c}{CCSD(T)}	&	\mc{3}{c}{CCSD(T)+LDA}	&	\mc{3}{c}{CCSD(T)+PBE}	\\ 
 							\cline{3-6}	\cline{7-9}	\cline{10-12}