correction Xavier for letter

BSEdyn.bib

@@ -1,13 +1,24 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-08-26 16:23:32 +0200 
+%% Created for Pierre-Francois Loos at 2020-08-31 14:41:43 +0200 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{Stuke_2020,
+	Author = {Annika Stuke and Christian Kunkel and Dorothea Golze and Milica Todorovi{\'c} and Johannes T. Margraf and Karsten Reuter and Patrick Rinke and Harald Oberhofer },
+	Date-Added = {2020-08-31 14:39:34 +0200},
+	Date-Modified = {2020-08-31 14:41:30 +0200},
+	Doi = {10.1038/s41597-020-0385-y},
+	Journal = {Sci. Data},
+	Pages = {58},
+	Title = {Atomic Structures and Orbital Energies of 61,489 Crystal-Forming Organic Molecules},
+	Volume = {7},
+	Year = {2020}}
+
 @article{Loos_2019c,
 	Author = {E. Giner and A. Scemama and J. Toulouse and P. F. Loos},
 	Date-Added = {2020-08-26 16:12:40 +0200},
@@ -17,7 +28,8 @@
 	Pages = {144118},
 	Title = {Chemically accurate excitation energies with small basis sets},
 	Volume = {151},
-	Year = {2019}}
+	Year = {2019},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.5122976}}
 
 @article{Liu_2020,
 	Author = {C. Liu and J. Kloppenburg and Y. Yao and X. Ren and H. Appel and Y. Kanai and V. Blum},
@@ -2403,7 +2415,8 @@
 @article{Strinati_1988,
 	Author = {Strinati, G.},
 	Date-Added = {2020-05-18 21:40:28 +0200},
-	Date-Modified = {2020-06-19 14:11:57 +0200},
+	Date-Modified = {2020-08-27 16:39:05 +0200},
+	Doi = {10.1007/BF02725962},
 	Journal = {Riv. Nuovo Cimento},
 	Pages = {1--86},
 	Title = {Application of the {{Green}}'s Functions Method to the Study of the Optical Properties of Semiconductors},

BSEdyn.tex

@@ -446,6 +446,7 @@ Substituting Eqs.~\eqref{eq:iL0bis}, \eqref{eq:spectral65}, and \eqref{eq:Xi_GW}
 \end{split}
 \end{equation}
 with $X_{jb,S} = \mel{N}{\ha_j^{\dagger} \ha_b}{N,S}$ and $Y_{jb,S} = \mel{N}{\ha_b^{\dagger} \ha_j}{N,S}$, and where $\kappa = 2 $ or $0$ for singlet and triplet excited states (respectively).
+\titou{This equation is identical to the one presented by Rohlfing and coworkers. \cite{Rohlfing_2000,Ma_2009a,Ma_2009b}}
 Neglecting the anti-resonant terms, $Y_{jb,S}$, in the dynamical BSE, which are (usually) much smaller than their resonant counterparts, $X_{jb,S}$, leads to the well-known TDA. 
 In Eq.~\eqref{eq:BSE-final}, 
 \begin{equation}
@@ -638,7 +639,7 @@ and
 \end{align}
 \end{subequations}
 
-According to perturbation theory, the $S$th BSE excitation energy and its corresponding eigenvector can then expanded as
+According to perturbation theory, the $S$th BSE excitation energy and its corresponding eigenvector can then be expanded as
 \begin{subequations}
 \begin{gather}
 	\Om{S}{} = \Om{S}{(0)} + \Om{S}{(1)} + \ldots,
@@ -733,7 +734,7 @@ Although it might be reduced to $\order*{\Norb^4}$ operations with standard reso
 All systems under investigation have a closed-shell singlet ground state.
 We then adopt a restricted formalism throughout this work.
 The $GW$ calculations performed to obtain the screened Coulomb operator and the quasiparticle energies are done using a (restricted) HF starting point.
-Perturbative $GW$ (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986,vanSetten_2013} quasiparticle energies are employed as starting points to compute the BSE neutral excitations.
+Perturbative $GW$ (or {\GOWO}) \cite{Hybertsen_1985a,Hybertsen_1986,vanSetten_2013} quasiparticle energies are employed as starting points to compute the BSE neutral excitations.
 These quasiparticle energies are obtained by linearizing the frequency-dependent quasiparticle equation, and the entire set of orbitals is corrected.
 Further details about our implementation of {\GOWO} can be found in Refs.~\onlinecite{Loos_2018b,Veril_2018}.
 Note that, for the present (small) molecular systems, {\GOWO}@HF and ev$GW$@HF yield similar quasiparticle energies and fundamental gap. 

Response_Letter/Response_Letter.tex

@@ -58,8 +58,16 @@ the authors do not compare their results with data obtained from
 plasmon-pole modelling. If they have such data readily available, 
 they might want to include them in the manuscript.}
 	\\
-	\alert{Sadly, it is hard to compare Rohlfing's results to ours as the molecules considered in Rohlfing's works are much larger than ours, the calculations are performed in non-conventional basis sets, and the underlying $GW$ calculations do not use the same starting point. 
-	We agree that, ultimately, it would be very interesting to test the performances of both approaches on the very same systems with the very same settings, but we feel this is outside the scope of the present study.}
+	\alert{The reviewer is correct. 
+	We go beyond Strinati's seminal work which was restricted to the TDA, and we attempt to provide to the reader more details about the derivation (see Eqs.~(12)-(18) and the Appendices), but indeed our dynamical BSE equations are eventually identical to the one provided by Rohlfing and coworkers. 
+	This is now restated again after Eq.~(21) where we write: 
+	``and triplet excited states (respectively). 
+	This equation is identical to the one presented by Rohlfing and coworkers.'' 
+	Further, the possible divergence of the ``beyond-TDA'' corrections forces us, as our colleagues Rohlfing and coworkers or Romaniello and coworkers, to stick to the TDA (this fact was not explicitly discussed in previous papers and we devote a small paragraph to that point). 
+	We really feel however that performing reference calculations on a large set of transitions, with well defined and standard basis sets, without the plasmon-pole approximation, and with comparison to reference calculations rather than experimental data, is an important step to better assess the merits of this ``simpler'' dynamical approach, before embarking into more sophisticated treatments. 
+	We did not implement the plasmon-pole approximation to perform a comparison with our exact (within RPA) dynamics for the reference molecules we study. 
+	There are actually many plasmon-pole models (Rohlfing-Kr\"uger-Pollman, Hybersten-Louie, Godby-Needs, etc.) and we feel that it is a full fledge study outside the scope of the present study to assess the merits of these various models. 
+	We hope that the availability of reference calculations that we provide may serve as a solid starting point to perform such studies.}
 	
 	\item
 {Concerning the other aspect, i.e. renormalization of the BSE 
@@ -140,7 +148,9 @@ The work is rigorous, carefully done and well presented. The dynamical correctio
 	This is not particularly clear and I encourage the authors to clarify this. 
 	For example, in Section E are equations 32 to 42 new or were they already derived by Rohlfing and others? }
 	\\
-	\alert{Equations 32 to 42 aren't new.
+	\alert{
+	We have clarified this point in the reply to Reviewer \#1 (see above). 
+	Equations 32 to 42 aren't new.
 	Originally, the dynamical correction has been derived by Strinati [see Ref.~(2) for a detailed derivation] but we have gone further by deriving also the anti-resonant term (see Sec. II.D.).
 	We have clarified this point in two places in the revised manuscript (Introduction and Conclusion).}
 
@@ -202,9 +212,11 @@ We hope to report a genuine dynamical treatment of the BSE in a forthcoming work
 	Or are they more pronounced, if $W$ has more structure in its frequency dependence? 
 }
 	\\
-	\alert{This equation now has a number.
-	Xavier this is for you.}
-	
+	\alert{
+	We thank the referee for his/her positive comment. 
+	This equation now has a number.
+	We indeed discussed the most obvious cases (CT and Rydberg excitations) for which the dynamical correction must be small but could not find convincing general arguments concerning i) the matrix elements associated with e.g. $\pi \to \pi^*$ versus $n \to \pi^*$ transitions, nor ii) with the dynamical part (energy denominators) of the correction. 
+	We prefer to keep our discussion as it is and avoid being too speculative at that stage.}
 	
 \end{itemize}