response letter

Response_Letter/Response_Letter.tex

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+\documentclass[10pt]{letter}
+\usepackage{UPS_letterhead,xcolor,mhchem,ragged2e,hyperref}
+\newcommand{\alert}[1]{\textcolor{red}{#1}}
+\definecolor{darkgreen}{HTML}{009900}
+
+
+\begin{document}
+
+\begin{letter}%
+{To the Editors of the Journal of Chemical Physics,}
+
+\opening{Dear Editors,}
+
+\justifying
+Please find attached a revised version of the manuscript entitled 
+\begin{quote}
+	\textit{``Connections between many-body perturbation and coupled-cluster theories''}.
+\end{quote}
+We thank the reviewers for their constructive comments and to support publication of the present manuscript.
+Our detailed responses to their comments can be found below.
+For convenience, changes are highlighted in red in the revised version of the manuscript. 
+
+We look forward to hearing from you.
+
+\closing{Sincerely, the authors.}
+
+\newpage
+
+%%% REVIEWER 1 %%%
+\noindent \textbf{\large Authors' answer to Reviewer \#1}
+
+
+
+{In this manuscript, Quintero-Monsebaiz et al. expand upon previously established connections between coupled-cluster (CC) theory and the random-phase approximation. 
+Specifically, they aim to connect CC theory to the Bethe-Salpeter equation (BSE) for neutral excitations and to the $GW$ approximation for charged (IP/EA) excitations, both of which have RPA screening at their heart. 
+The manuscript is well-written and contributes to a growing body of literature comparing, theoretically and numerically, the performance of wavefunction and Green's function-based many-body theories. 
+J. Chem. Phys. is a good venue for this work, and I am happy to recommend publication, although I have a few suggestions for the authors to consider.
+}
+\\
+\alert{
+bla bla bla
+}
+
+\begin{enumerate}
+
+\item 
+{How should I understand the BSE correlation energy and the plasmon trace formula given in Eq.~(9)? 
+The BSE is an approximation to the two-particle Green's function, which completely determines the two-particle reduced density matrix. 
+From this, I could obtain the total energy by contraction with one- and two-electron Hamiltonian matrix elements. 
+Can this viewpoint be related precisely to the trace formula (9)? 
+If so, I think a few words to make this connection would be valuable to the reader. 
+It's not obvious (to me at least) that all methods that allow a Tamm-Dancoff approximation can rigorously be related to a correlation energy expression in the form of the plasmon trace formula.}
+\\
+\alert{
+bla bla bla
+}
+
+\item 
+{Concerning the discussion below Eq.~(23): I note that the ``$GW$ pre-treatment'' renormalizes the one-electron energies via more than mosaic diagrams. 
+The mosaic diagrams are the only ones that are captured at the CCSD level, but in general, the $GW$ approximation also has a forward-time-ordered screened exchange interaction mediated by particle-hole pairs (requiring more than CCSD).
+}
+\\
+\alert{
+bla bla bla
+}
+
+\item 
+{In general, Eq.~(24) defines all poles of the one-particle Green's function, although the surrounding discussion suggests that only quasiparticle excitations are found in this manner. 
+(I'm sure the authors appreciate this point, as made clear elsewhere in the manuscript).
+}
+\\
+\alert{
+bla bla bla
+}
+
+\item 
+{I quite like the discussion beginning with Eq.~(29), but it makes me wonder about the major findings of the present manuscript. 
+Specifically, I think this manuscript exploits the following numerical observation. 
+Consider any eigenvalue problem and partition it into two spaces,
+
+Assuming existence of the inverse, this can be trivially rewritten as an eigenvalue problem for a matrix in the “A” subspace,
+where $T = Y X^{-1}$. Of course, this is not useful without $T$. So what determines T without access to all the eigenvectors contained in X, Y? We can rewrite the two equations contained in (1) as
+or, upon combining the above equations,
+The above is some nonlinear equation that can be solved for the unknown T. It looks superficially like a CCSD equation (which could be solved, e.g., by iteration), but clearly there is no formal connection. Does the fact that any linear eigenvalue equation can be partitioned to produce a nonlinear eigenvalue equation, or equivalently recast into the determination of the solution to a system of nonlinear equations, imply any formal connection with CC theory (as the section title implies)? Or is it a mathematically interesting observation that indicates an alternative route toward the determination of eigenvalues from a partitioned matrix?
+As far as I can tell, the above general observation is applied in two distinct settings to derive the results in the present manuscript. For the BSE, the partitioning is used to eliminate the “deexcitation” space, similar to its elimination in the RPA problem. For the GW approximation, the partitioning is used to eliminate the 2h1p/2p1h space. However, I reemphasize that in both cases, the “CC-like” equations that result are analogous to ground-state CC theory, and so the formal connection between the theories is tenuous.
+}
+\\
+\alert{
+bla bla bla
+}
+
+\item 
+{A confusion I have in my own discussion above is related to a question I have about the final Eq.~(34) of the present work. 
+Where was the approximation made that indicates that this only finds the $N$ principle excitation energies? 
+I agree that $\epsilon + \Sigma$ is only $N \times N$ so it should only have $N$ eigenvalues. 
+But all equations were exact, assuming existence of the inverse. 
+What am I missing here? 
+If the authors appreciate this confusion, then some discussion in the manuscript would be welcome.}
+\\
+\alert{
+bla bla bla
+}
+
+\end{enumerate}
+
+%%% REVIEWER 2 %%%
+\noindent \textbf{\large Authors' answer to Reviewer \#2}
+
+{This manuscript builds on recent analytic work, drawing connections and deepening understanding between different electronic structure methods, specifically for excitations. 
+The work is self-contained, coherent and concise. 
+I cannot fault the presentation of the analytic results, their correctness, or the interpretation and understanding that can be drawn from them. 
+I would recommend acceptance without reservation.}
+\\
+\alert{
+bla bla bla
+}
+
+
+\end{letter}
+\end{document}

Response_Letter/UPS_letterhead.sty

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+%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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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+\evensidemargin  0.25in
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+\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}