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\begin{letter}%
{To the Editors of the Journal of Chemical Theory and Computation}

\opening{Dear Editors,}

\justifying
Please find attached a revised version of the manuscript entitled 
\begin{quote}
\textit{``A Density-Based Basis-Set Incompleteness Correction for GW Methods''}.
\end{quote}
We would to thank the reviewers for their constructive comments.
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 hope that you will agree that our manuscript is now suitable for publication in JCTC.

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 present an exciting piece of work with what seems to be an efficient, and ``possibly  simpler'' than F12-RI, technique  to accelerate convergency with respect to basis set size in the case of GW quasiparticle energy calculations. The DFT-based correction towards the CBS limit was introduced in previous papers in the case of the total correlation energy. Considering the total energy as a functional of the one-body Green's function allows to bridge total energies and self-energy using functional derivative techniques. The results are rather impressive, demonstrating that corrected triple-zeta calculations are equivalent for small systems to quintuple-zeta ones. 
	The paper is thus clearly within the scope of the Journal of Chemical Theory and Computation, presents original work that may prove useful to a large community. The referee recommends publication provided that the authors seriously consider the following suggestions/questions.}
	\\
	\alert{bla bla.}

	\item 
	{The main criticism as a reader is that all details of the construction of the total energy correction to the "finite-size basis difference" with respect to the CBS limit is absent from the paper (very short Section II-C).  The authors refer the reader to previous publications (mainly [57]) dealing with total energies in a CCSD(T) quantum chemistry wavefunction framework with which the Green's function community may not be very familiar with.  In particular the construction of a local range-separation parameter related to the diagonal of the ``effective'' 2-electron-operator-in-a-basis  ($W^{\beta}$) would deserve to be somehow explained in the present paper.}
	\\
	\alert{bla bla.}
	
	\item 
	{Following the previous question, and from a pragmatic point of view, what is needed as an input to construct this basis-set-incompleteness correction, namely this effective local potential of Eq. [31] ? Again the answer is present in equations 4-9 of Ref. [57] but could be summarised in the present paper and possibly simplified in the present case of a perturbation theory based on a input mono-determinental Kohn-Sham or HF description of the many-body wavefunction. This may also give an hint on the cost (scaling) and complexity of the approach. }
	\\
	\alert{bla bla.}
	
	\item 
	{As a corollary to this comment, the referee is still surprised that one may build a ``universal'' correction, in a sens that the same correction would apply to any approximation to the self-energy (if the referee understands correctly ...) whatever the diagrams used. If this is a correct statement, this should be emphasised and probably better commented.}	
	\\
	\alert{bla bla.}	

	\item 
	{Minor: The referee is somehow surprised by the IP CCSD(T) values for cytosine and uracil in table III which are noticeably much larger than the experiment, in contrast with the other nucleobases.  As a matter of fact the CCSD(T) values by Roca-Sanjuan et al (JCP 2006) agree reasonably with the values reported by the authors for adenine, guanine, thymine, but are completely off for cytosine and uracil. Could the authors check and potentially comment.}
	\\
	\alert{bla bla.}
	
\end{itemize}

%%% REVIEWER 2 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#2}

\begin{itemize}
	\item 
	{I enjoyed reading the manuscript and am of the opinion that it presents an important contribution to the field addressing one of the main bottlenecks that the GW approach is infamous for, the slow basis set convergence. There are a few issues however that the authors should address}
	\\
	\alert{bla bla.}
	
	\item 
	{The authors discuss GW in depth in sections II.A and II.B. For me however the novelty in this paper is all about what is in section II.C. We are given references there but to me C should be extended to provide more information.}
	\\
	\alert{bla bla.}
	
	\item 
	{in Section III the authors mention that the infinitesimal eta is put to 0. This is physically incorrect. eta is a positive infinitesimal and cannot be just put to zero. Numerically it has been shown that indeed the self energy becomes discontinuous by doing so. This is the main reason for the low quality rating. }
	\\
	\alert{bla bla.}
	
	\item 
	{Figures 1, and the corresponding figures in the supplementry are plotted on a linear scale of X. Personally I think it is much more instructive to plot agains X-3, which wil much clearer visualize convergence. }	
	\\
	\alert{bla bla.}	
	
	\item 
	{The comparison in table II is made against a CBS limit extrapolating local basis sets. 10.1021/acs.jctc.7b00952 also provides planewave basis set extrapolated results for the gw100 set. It may be interesting to include this in the comparison.}	
	\\
	\alert{bla bla.}
	
	\item 
	{Finally, as a very general point I thinks paper reporting large amounts of data, where the amount of data in this paper for me clearly qualifies as large, should also provide the data in a machine readable format. a json, hdf5 of netcdf4 format would be a good standard, a csv would be minimal.}	
	\\
	\alert{bla bla.}
\end{itemize}

\end{letter}
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