Modifs toto

Response_Letter/Response_Letter.tex

@@ -91,6 +91,7 @@ We look forward to hearing from you.
 	It would be valuable to the work if the authors were to indicate the variance with respect to the number of points used in the extrapolations; in the linear extrapolations, one could use, say, between 3-5 points, whereas between 4-6 points could be used in the quadratic fits? 
 	In any case, the authors should comment (in more detail) on their choice of fitting function and number of data points.}
 	\\
+%TITOU : -863.1(11) ca veut dire  -836.1 +/- 0.11  ou  -836.1 +/- 1.1 ?
 	\alert{Using the last 3, 4, 5, and 6 points (i.e., the largest wave functions), linear extrapolations yield the following correlation energy estimates: $-863.1(11)$, $-863.4(5)$, $-862.1(8)$, and $-863.5(11)$ mE$_h$, respectively, where the fitting error is reported in parenthesis. 
 	These numbers vary by $1.4$ mE$_h$.
 	The four-point extrapolated estimate that we have chosen to report as our best estimate corresponds to the smallest fitting error.
@@ -112,7 +113,7 @@ We look forward to hearing from you.
 	{It would be interesting if the authors could comment (even speculatively) on why results in the localized FB basis are significantly lower (and hence, in the authors' own words, more trustworthy) than the corresponding results in the NO basis.}
 	\\
 	\alert{Localized orbitals significantly speed up the convergence of SCI calculations by taking benefit of the local character of the electron correlation.
-	We have mentioned this in the revised manuscript and added two references discussing the use of localized orbitals in SCI calculations (Refs.~65 and 66).}
+	We have mentioned this in the revised manuscript and added references discussing the use of localized orbitals \textit{vs} natural orbitals in CI calculations (Refs.~65--69).}
 	
 	\item 
 	{Why are the rMP2-based corrections considered superior to the corresponding corrections based on MP2? 
@@ -134,7 +135,7 @@ We look forward to hearing from you.
 	\\
 	\alert{Boys-Foster is the only localization criterion available at the moment but we are planning on implementing other schemes in the near future.
 	That being said, because we group the MOs by symmetry classes (see footnote 63), our localization procedure ensures the $\sigma$-$\pi$ separability, like in PM.
-	This would not be possible in general but, thanks to the high symmetry of benzene, it is feasable in the present case.
+	This would not be possible in general but, thanks to the high symmetry of benzene, it is feasible in the present case.
 	}
 	
 	\item 

benzene.bib

@@ -20,6 +20,52 @@
 	Year = {2011},
 	Bdsk-Url-1 = {https://doi.org/10.1063/1.3600351}}
 
+@article{Suaud_2017,
+    author = {Suaud, Nicolas and Malrieu, Jean-Paul},
+    title = {{Natural molecular orbitals: limits of a Lowdin's conjecture}},
+    journal = {Mol. Phys.},
+    volume = {115},
+    number = {21-22},
+    pages = {2684--2695},
+    year = {2017},
+    month = {Nov},
+    issn = {0026-8976},
+    publisher = {Taylor {\&} Francis},
+    doi = {10.1080/00268976.2017.1303207}
+}
+
+@article{Angeli_2009,
+    author = {Angeli, Celestino},
+    title = {{On the nature of the π {$\rightarrow$} π{$\ast$} ionic excited states: The
+    V state of ethene as a prototype}},
+    journal = {J. Comput. Chem.},
+    volume = {30},
+    number = {8},
+    pages = {1319--1333},
+    year = {2009},
+    month = {Jun},
+    issn = {0192-8651},
+    publisher = {John Wiley {\&} Sons, Ltd},
+    doi = {10.1002/jcc.21155}
+}
+
+@article{Angeli_2003,
+    author = {Angeli, Celestino and Calzado, Carmen J. and 
+    Cimiraglia, Renzo and Evangelisti, Stefano and Guih\'ery, Nathalie and 
+    Leininger, Thierry and Malrieu, Jean-Paul and Maynau, Daniel and 
+    Ruiz, Jos\'e Vicente Pitarch and Sparta, Manuel},
+    title = {{The use of local orbitals in multireference calculations}},
+    journal = {Mol. Phys.},
+    volume = {101},
+    number = {9},
+    pages = {1389--1398},
+    year = {2003},
+    month = {May},
+    issn = {0026-8976},
+    publisher = {Taylor {\&} Francis},
+    doi = {10.1080/0026897031000082149}
+}
+
 @article{Deustua_2017,
 	Author = {Deustua, J. Emiliano and Shen, Jun and Piecuch, Piotr},
 	Date-Added = {2020-10-09 12:21:32 +0200},

benzene.tex

@@ -143,7 +143,7 @@ higher-lying $\pi$ [39,41--43,46,49,50,53--57,71--74,82--85,87,92,93,98];
 higher-lying $\sigma$ [37,38,40,44,45,47,48,51,52,58--70,75--81,86,88--91,94--97,99--114].}
 Like Pipek-Mezey, \cite{Pipek_1989} this choice of orbital windows allows to preserve a strict $\sigma$-$\pi$ separation in planar systems like benzene.
 As one can see from the energies of Table \ref{tab:NOvsLO}, for a given value of $N_\text{det}$, the variational energy as well as the PT2-corrected energies are much lower with localized orbitals than with natural orbitals. 
-\alert{Indeed, localized orbitals significantly speed up the convergence of SCI calculations by taking benefit of the local character of electron correlation.\cite{BenAmor_2011,Chien_2018,Eriksen_2020}}
+\alert{Indeed, localized orbitals significantly speed up the convergence of SCI calculations by taking benefit of the local character of electron correlation.\cite{Angeli_2003,Angeli_2009,BenAmor_2011,Suaud_2017,Chien_2018,Eriksen_2020}}
 We, therefore, consider these energies more trustworthy, and we will base our best estimate of the correlation energy of benzene on these calculations. 
 The convergence of the CIPSI correlation energy using localized orbitals is illustrated in Fig.~\ref{fig:CIPSI}, where one can see the behavior of the correlation energy, $\Delta E_\text{var.}$ and $\Delta E_\text{var.} + E_\text{(r)PT2}$, as a function of $N_\text{det}$ (left panel).
 The right panel of Fig.~\ref{fig:CIPSI} is more instructive as it shows $\Delta E_\text{var.}$ as a function of $E_\text{(r)PT2}$, and their corresponding four-point linear extrapolation curves that we have used to get our final estimate of the correlation energy.