response letter with clotilde comments

Manuscript/FarDFT.bib

@@ -1,13 +1,23 @@
 %% This BibTeX bibliography file was created using BibDesk.
 %% http://bibdesk.sourceforge.net/
 
-%% Created for Pierre-Francois Loos at 2020-05-10 19:45:36 +0200 
+%% Created for Pierre-Francois Loos at 2020-05-19 16:23:00 +0200 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
 
+@article{Fromager_2020,
+	Archiveprefix = {arXiv},
+	Author = {Emmanuel Fromager},
+	Date-Added = {2020-05-13 07:41:14 +0200},
+	Date-Modified = {2020-05-13 07:41:14 +0200},
+	Eprint = {2001.08605},
+	Primaryclass = {physics.chem-ph},
+	Title = {Individual correlations in ensemble density-functional theory: State-driven/density-driven decomposition without additional Kohn-Sham systems},
+	Year = {2020}}
+
 @article{Refaely-Abramson_2012,
 	Author = {Sivan Refaely-Abramson and Sahar Sharifzadeh and Niranjan Govind and Jochen Autschbach and Jeffrey B. Neaton and Roi Baer and Leeor Kronik},
 	Date-Added = {2020-05-03 21:27:34 +0200},
@@ -252,14 +262,14 @@
 	Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package},
 	Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}}
 
-@article{Fromager_2020,
+@article{Loos_2020,
 	Archiveprefix = {arXiv},
-	Author = {Emmanuel Fromager},
+	Author = {P. F. Loos and E. Fromager},
 	Date-Added = {2020-04-08 14:13:18 +0200},
-	Date-Modified = {2020-04-08 14:13:18 +0200},
+	Date-Modified = {2020-05-13 07:41:52 +0200},
-	Eprint = {2001.08605},
+	Eprint = {2003.05553},
 	Primaryclass = {physics.chem-ph},
-	Title = {Individual correlations in ensemble density-functional theory: State-driven/density-driven decomposition without additional Kohn-Sham systems},
+	Title = {A weight-dependent local correlation density-functional approximation for ensembles},
 	Year = {2020}}
 
 @article{Bottcher_1974,
@@ -328,15 +338,6 @@
 	Volume = {112},
 	Year = {2008}}
 
-@article{Loos_2020,
-	Author = {P. F. Loos and E. Fromager},
-	Date-Added = {2020-04-07 10:59:44 +0200},
-	Date-Modified = {2020-04-07 11:01:30 +0200},
-	Journal = {J. Chem. Phys.},
-	Pages = {arXiv:2003.05553},
-	Title = {A weight-dependent local correlation density-functional approximation for ensembles},
-	Year = {submitted}}
-
 @article{Lindh_2001,
 	Author = {R. Lindh and P.-A. Malmqvist and L. Gagliardi},
 	Date-Added = {2020-03-30 09:59:22 +0200},
@@ -5267,10 +5268,10 @@
 	Volume = {41},
 	Year = {1990}}
 
-@article{Loos_2018,
+@article{Loos_2018b,
 	Author = {P. F. Loos and A. Scemama and A. Blondel and Y. Garniron and M. Caffarel and D. Jacquemin},
 	Date-Added = {2018-10-24 22:38:52 +0200},
-	Date-Modified = {2020-04-10 22:19:17 +0200},
+	Date-Modified = {2020-05-19 14:01:04 +0200},
 	Doi = {10.1021/acs.jctc.8b00406},
 	Journal = {J. Chem. Theory Comput.},
 	Pages = {4360},

Manuscript/FarDFT.tex

@@ -188,7 +188,7 @@ In other words, memory effects are absent from the xc functional which is assume
 Third and more importantly in the present context, a major issue of
 TD-DFT actually originates directly from the choice of the (ground-state) xc functional, and more specifically, the possible (not to say likely) substantial variations in the quality of the excitation energies for two different choices of xc functionals.
 
-Because of its popularity, approximate TD-DFT has been studied in excruciated details by the community, and some researchers have quickly unveiled various theoretical and practical deficiencies.
+Because of its popularity, approximate TD-DFT has been studied extensively by the community, and some researchers have quickly unveiled various theoretical and practical deficiencies.
 For example, TD-DFT has problems with charge-transfer \cite{Tozer_1999,Dreuw_2003,Sobolewski_2003,Dreuw_2004,Maitra_2017} and Rydberg \cite{Tozer_1998,Tozer_2000,Casida_1998,Casida_2000,Tozer_2003} excited states (the excitation energies are usually drastically underestimated) due to the wrong asymptotic behaviour of the semi-local xc functional.
 The development of range-separated hybrids provides an effective solution to this problem. \cite{Tawada_2004,Yanai_2004} 
 From a practical point of view, the TD-DFT xc kernel is usually considered as static instead of being frequency dependent.
@@ -483,7 +483,7 @@ linear ensemble energy and, hence, the same value of the excitation energy indep
 	\includegraphics[width=\linewidth]{fig1}
 	\caption{
 	\ce{H2} at equilibrium bond length: deviation from linearity of the ensemble energy $\E{}{\ew{}}$ (in hartree) as a function of $\ew{}$ for various functionals and the aug-cc-pVTZ basis set.
-	See main text for the definition of the various functional's acronyms.
+	See main text for the definition of the various functionals' acronyms.
 	\label{fig:Ew_H2}
 	}
 \end{figure}
@@ -494,7 +494,7 @@ linear ensemble energy and, hence, the same value of the excitation energy indep
 	\includegraphics[width=\linewidth]{fig2}
 	\caption{
 	\ce{H2} at equilibrium bond length: error (with respect to FCI) in the excitation energy $\Ex{}{(2)}$ (in eV) associated with the doubly-excited state as a function of $\ew{}$ for various functionals and the aug-cc-pVTZ basis set.
-	See main text for the definition of the various functional's acronyms.
+	See main text for the definition of the various functionals' acronyms.
 	\label{fig:Om_H2}
 	}
 \end{figure}
@@ -585,7 +585,7 @@ We shall come back to this point later on.
 \subsubsection{Weight-independent correlation functional}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-Third, we add up correlation effects via the conventional VWN5 local correlation functional. \cite{Vosko_1980}
+Third, we include correlation effects via the conventional VWN5 local correlation functional. \cite{Vosko_1980}
 For the sake of clarity, the explicit expression of the VWN5 functional is not reported here but it can be found in Ref.~\onlinecite{Vosko_1980}.
 The combination of the (weight-independent) Slater and VWN5 functionals (SVWN5) yield a highly convex ensemble energy (green curve in Fig.~\ref{fig:Ew_H2}), while the combination of CC-S and VWN5 (CC-SVWN5) exhibit a smaller curvature and improved excitation energies (red curve in Figs.~\ref{fig:Ew_H2} and \ref{fig:Om_H2}), especially at small weights, where the CC-SVWN5 excitation energy is almost spot on. 
 

Response_Letter/Response_Letter.tex

@@ -0,0 +1,97 @@
+\documentclass[10pt]{letter}
+\usepackage{UPS_letterhead,xcolor,mhchem,mathpazo,ragged2e,hyperref}
+\newcommand{\alert}[1]{\textcolor{red}{#1}}
+\definecolor{darkgreen}{HTML}{009900}
+
+
+\begin{document}
+
+\begin{letter}%
+{To the Members of the Faraday Discussions Scientific Committee,}
+
+\opening{Dear Members of the Faraday Discussions Scientific Committee,}
+
+\justifying
+Please find attached a revised version of the manuscript entitled 
+\begin{quote}
+\textit{``Weight Dependence of Local Exchange-Correlation Functionals in Ensemble Density-Functional Theory: Double Excitations in Two-Electron Systems''}.
+\end{quote}
+We thank the reviewer for his/her constructive comments.
+Our detailed responses to his/her comments can be found below.
+
+We look forward to hearing from you.
+
+\closing{Sincerely, the authors.}
+
+%%% REVIEWER 1 %%%
+\noindent \textbf{\large Authors' answer to Reviewer \#1}
+
+\begin{itemize}
+
+	\item
+	{The authors describe the ensemble formulation of DFT or the Gross-Oliveira-Kohn DFT (GOK-DFT) in its Kohn-Sham formulation as a viable method for excited state calculations. They provide a very clear summary of the theory, followed by the main work of the paper which is the investigation of weight-dependent LDA-type xc functionals for eDFT calculations. The provide important insights on small systems with 2 electrons and functionals that are tailored for double excitations in these systems. The manuscript makes an important contribution to the field of DFT and should be accepted for publication. However, I would be grateful if the authors modify the paper slightly to address the following minor points and corrections:}
+	\\
+	\alert{We thank the reviewer for his/her kind comments. 
+	His/her comments are addressed below.}
+
+	\item 
+	{They should comment about what is needed (or even if it is possible) to develop a weight-dependent universal xc functional for eDFT calculations instead of application-specific functionals as presented in this paper.}
+	\\
+	\alert{bla bla bla}
+
+	\item 
+	{In the captions of Figures 1 and 2 replace "functional's" with "functionals'"}
+	\\
+	\alert{This has been fixed.}
+
+	\item 
+	{The density $n(r)$ used in equation 21, 9, 10 and more doesn't represent any specific density. 
+	In the case of equation 21, we simply present the well-known Dirac-exchange density functional and, by definition of a density functional, we don't have to specify in its formulation to which density it is applied but only that it is a mathematical object applying to any density $n(r)$.
+Of course, when we will use this functional or any other one in our work we will surely apply it to the ensemble Density $n^w(r)$ and the notation will be carefully modified accordingly. }
+	
+	\item 
+	{Change "Third, we add up correlation effects" to "Third, we include correlation effects"}	
+	\\
+	\alert{ This has been fixed.}	
+
+	
+	\item 
+	{Change "studied in excruciated details" to "studied extensively"}	
+	\\
+	\alert{ This has been fixed.}	
+	
+		
+	\item 
+	{They need to be a bit more consistent with their notation as in equation 9 and elsewhere "$n(r)$" should be the ensemble (weight-dependent) density "$n^w(r)$". 
+	I don?t believe they defined "$n(r)$" in the paper so I don?t know which density it represents. }	
+	\\
+	\alert{See our response to 6.}	
+		
+	\item 
+	{Even if it sounds trivial, they should explain why the exact xc functional should have linear dependence in the excitation energies as a function of the weight value.}	
+	\\
+	\alert{GOK variational principle states that the expectation value of the ensemble energy admits/possesses a lower bond which is linear with respect to each of the ensemble-weights $w_i$ and is the exact ensemble energy of the studied system (equation 1). 
+	Moreover, by construction, one can easily see that the slope of the exact ensemble energy with respect to a specific weight $w_i$ corresponds to the excitation energy of the system defined between the ground state and the ith-excited state associated to this specific weight (equation 4). 
+	It is important that the reader keeps in mind that the exact excitation energies are based on pure-state energies and, therefore, do not depend on the weights of the ensemble.
+	In practice, the ensemble energy is rarely w-linear (linear in w ?) because of the use of approximate xc-functionals. 
+	Indeed, by inserting the ensemble density in the Hartree interaction functional (equation 9), it introduces spurious quadratic curvature with respect to the weight in the ensemble energy. 
+	Some of those terms are responsible of the unphysical phenomenon called ghost-interaction errors. 
+	Therefore, the ensemble-Khon-Sham gap obtained at the end of the ensemble-HF-calculation is, somehow, "weight-contaminated" and doesn't possess the right weight-dependence. 
+	(two first terms of the right-hand side of equation16)
+	By taking its first derivative with regard to the weight, the xc-functional is expected to compensate those parasite-quadratic terms in order to retrieve the linear behavior of the exact ensemble energy and one can understand that only a weight-dependant xc-functional could do so.
+	At the best of my knowledge, I cannot see any reason why the xc-functional should be w-linear. 
+	The important idea is that the linearity must be in the ensemble energy but the main constraint on the xc-functional should be that it is weight-dependant.
+	We emphasize that only the exact ensemble-xc-functional would have the ideal weight-dependency that would make the corresponding ensemble energy reproduce perfectly the linear behavior of the exact ensemble energy and lead to weight-independant excitation energies, that is exact excitation energies.
+	The use of an approximate weight-dependant xc-functional could reduce the ensemble energy curvature and give less weight-dependant excitation energies but it is reasonable to admit that it also could make things worse it the weight-dependency of the functional is poorly chosen.
+	That is why the construction of "good" weight-dependant xc-functionals is a really challenging matter in eDFT.}	
+	
+\end{itemize}
+
+\end{letter}
+\end{document}
+
+
+
+
+
+

Response_Letter/UPS_letterhead.sty

@@ -0,0 +1,70 @@
+%ANU etterhead Yves
+%version 1.0	12/06/08
+%need to be improved
+
+
+\RequirePackage{graphicx}
+
+%%%%%%%%%%%%%%%%%%%%% DEFINE USER-SPECIFIC MACROS BELOW %%%%%%%%%%%%%%%%%%%%%
+\def\Who     {Pierre-Fran\c{c}ois Loos}
+\def\What    {Dr}
+\def\Where   {Universit\'e Paul Sabatier}
+\def\Address {Laboratoire de Chimie et Physique Quantiques}
+\def\CityZip {Toulouse, France}
+\def\Email   {loos@irsamc.ups-tlse.fr}
+\def\TEL     {+33 5 61 55 73 39}
+\def\URL     {} % NOTE: use $\sim$ for tilde
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MARGINS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\textwidth       6in
+\textheight      9.25in
+\oddsidemargin   0.25in
+\evensidemargin  0.25in
+\topmargin       -1.50in
+\longindentation 0.50\textwidth
+\parindent       5ex
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%% ADDRESS MACRO BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\address{
+    \includegraphics[height=0.7in]{CNRS_logo.pdf}     \hspace*{\fill}\includegraphics[height=0.7in]{UPS_logo.pdf}
+	\\
+	\hrulefill
+	\\
+	{\small \What~\Who\hspace*{\fill} Telephone:\ \TEL
+	\\
+	\Where\hspace*{\fill}  Email:\ \Email
+	\\
+	\Address\hspace*{\fill}
+	\\
+	\CityZip\hspace*{\fill} \URL}
+	 }
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%% OTHER MACROS BELOW %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\signature{\What~\Who}
+
+\def\opening#1{\ifx\@empty\fromaddress
+ \thispagestyle{firstpage}
+ \hspace*{\longindendation}\today\par
+ \else \thispagestyle{empty}
+ {\centering\fromaddress \vspace{5\parskip} \\
+\today\hspace*{\fill}\par}
+ \fi
+ \vspace{3\parskip}
+ {\raggedright \toname \\ \toaddress \par}\vspace{3\parskip}
+ \noindent #1\par\raggedright\parindent 5ex\par
+ }
+
+%I do not know what does the macro below
+
+%\long\def\closing#1{\par\nobreak\vspace{\parskip}
+ %\stopbreaks
+ %\noindent
+ %\ifx\@empty\fromaddress\else
+ %\hspace*{\longindentation}\fi
+ %\parbox{\indentedwidth}{\raggedright
+ %\ignorespaces #1\vskip .65in
+ %\ifx\@empty\fromsig
+ %\else \fromsig \fi\strut}
+ %\vspace*{\fill}
+% \par}