a few changes

Manuscript/GW-srDFT.tex

@@ -350,7 +350,7 @@ For example, if the reference is Hartree-Fock ($\HF$), $\Sig{\text{ref}}{\Bas}(\
 
 In this subsection, we provide the minimal set of equations required to describe {\GOWO}.
 More details can be found, for example, in Refs.~\citenum{vanSetten_2013, Kaplan_2016, Bruneval_2016}.
-For the sake of simplicity, we consider closed-shell systems with a $\KS$ single-particle reference.
+For the sake of simplicity, we only give the equations for closed-shell systems with a $\KS$ single-particle reference.
 The one-electron energies $\e{p}$ and their corresponding (real-valued) orbitals $\MO{p}(\br{})$ (which defines the basis set $\Bas$) are then $\KS$ energies and orbitals.
 
 Within the {\GW} approximation, the correlation part of the self-energy reads 
@@ -365,16 +365,16 @@ Within the {\GW} approximation, the correlation part of the self-energy reads
 	& + 2 \sum_{a}^\text{virt} \sum_{m} \frac{[pa|m]^2}{\omega - \e{a} - \Om{m} + i \eta},
 \end{split}
 \end{equation}
-where $m$ corresponds to a sum over the single excitations and $\eta$ is a positive infinitesimal.
+where $m$ labels excited states and $\eta$ is a positive infinitesimal.
 The screened two-electron integrals
 \begin{equation}
-	[pq|m] = \sum_{ia} (pq|ia) (\bX+\bY)_{ia}^{m}
+	[pq|m] = \sum_{ia} (pq|ia) (\bX_m+\bY_m)_{ia}
 \end{equation}
 are obtained via the contraction of the bare two-electron integrals \cite{Gill_1994} 
 \begin{equation}
 	(pq|rs) = \iint \frac{\MO{p}(\br{}) \MO{q}(\br{}) \MO{r}(\br{}') \MO{s}(\br{}')}{\abs*{\br{} - \br{}'}} \dbr{} \dbr{}',
 \end{equation}
-and the transition densities $(\bX+\bY)_{ia}^{m}$ originating from a (direct) random phase approximation (RPA) calculation \cite{Casida_1995, Dreuw_2005}
+and the transition densities $(\bX_m+\bY_m)_{ia}$ originating from a (direct) random-phase approximation (RPA) calculation \cite{Casida_1995, Dreuw_2005}
 \begin{equation}
 \label{eq:LR}
 	\begin{pmatrix}
@@ -382,20 +382,20 @@ and the transition densities $(\bX+\bY)_{ia}^{m}$ originating from a (direct) ra
 		-\bB	&	-\bA	\\
 	\end{pmatrix}
 	\begin{pmatrix}
-		\bX	\\
+		\bX_m	\\
-		\bY	\\
+		\bY_m	\\
 	\end{pmatrix}
 	=
-	\bOm
+	\Om{m}
 	\begin{pmatrix}
-		\bX	\\
+		\bX_m	\\
-		\bY	\\
+		\bY_m	\\
 	\end{pmatrix},
 \end{equation}
 with
 \begin{align}
 \label{eq:RPA}
-	A_{ia,jb} & = \delta_{ij} \delta_{ab} (\e{a} - \e{i}) + 2 (ib|aj),
+	A_{ia,jb} & = \delta_{ij} \delta_{ab} (\e{a} - \e{i}) + 2 (ia|bj),
 	&
 	B_{ia,jb} & = 2 (ia|jb),
 \end{align}

Manuscript/SI/GW-srDFT-SI.tex

@@ -155,6 +155,7 @@
 \newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
 \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
 \newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
+\newcommand{\IUF}{Institut Universitaire de France, Paris, France}
 
 \begin{document}	
 
@@ -163,7 +164,7 @@
 \author{Pierre-Fran\c{c}ois Loos}
 \email[Corresponding author: ]{loos@irsamc.ups-tlse.fr}
 \affiliation{\LCPQ}
-\author{Bath\'elemy Pradines}
+\author{Barth\'el\'emy Pradines}
 \affiliation{\LCT}
 \affiliation{\ISCD}
 \author{Anthony Scemama}
@@ -173,6 +174,7 @@
 \author{Julien Toulouse}
 \email[Corresponding author: ]{toulouse@lct.jussieu.fr}
 \affiliation{\LCT}
+\affiliation{\IUF}
 
 \begin{abstract}
 \end{abstract}
@@ -182,7 +184,7 @@
 \begin{figure*}
 	\includegraphics[width=\linewidth]{IP_G0W0HF}
 	\caption{
-	IPs (in eV) computed at the {\GOWO}@HF (black circles), {\GOWO}@HF+srLDA (red squares) and {\GOWO}@HF+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set. 
+	IPs (in eV) computed at the {\GOWO}@HF (black circles), {\GOWO}@HF+srLDA (red squares), and {\GOWO}@HF+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z) for the 20 smallest molecules of the GW100 set. 
 	The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
 	\label{fig:IP_G0W0HF}
 	}
@@ -191,7 +193,7 @@
 \begin{figure*}
 	\includegraphics[width=\linewidth]{IP_G0W0PBE0}
 	\caption{
-	IPs (in eV) computed at the {\GOWO}@PBE0 (black circles), {\GOWO}@PBE0+srLDA (red squares) and {\GOWO}@PBE0+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ and cc-pV5Z) for the 20 smallest molecules of the GW100 set. 
+	IPs (in eV) computed at the {\GOWO}@PBE0 (black circles), {\GOWO}@PBE0+srLDA (red squares), and {\GOWO}@PBE0+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets (cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z) for the 20 smallest molecules of the GW100 set. 
 	The thick black line represents the CBS value obtained by extrapolation with the three largest basis sets.
 	\label{fig:IP_G0W0HF}
 	}