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\begin{letter}%
{To the Editors of Journal of Physical Chemistry Letters}

\justifying
\opening{Dear Editors,}

Please find attached a revised version of the manuscript entitled 
{\it "A Density-Based Basis-Set Correction For Wave Function Theory"}.

We would to thank the reviewers for their constructive comments.
Our detailed responses to their comments can be found below.
For convenience, all modifications and 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 JPCL.

We look forward to hearing from you.

\closing{Sincerely, the authors.}

\newpage

%%% REVIEWER 1 %%%
\noindent \textbf{\large Authors' answer to Reviewer \#1}

\begin{itemize}
	\item 
	\textit{This manuscript reports a major advance in electronic structure theory, by providing a cheap and mathematically motivated correction for finite basis size effects in high-level theories. 
	I expect it to have immediate applications among users, certainly once user friendly code is released. 
	The work is definitely worthy of being published in JPCL, after changes. 
	That said, for the reasons explained below, I think the current manuscript requires changes somewhere between major and minor.}
	
	\item 
	\textit{My main issue with the manuscript is that it is not sufficiently well self-contained or explained. 
	Being familiar with previous work on the topic, I was mostly able to follow the manuscript without hassle. 
	Someone without familiarity would struggle. 
	For example, the authors refer several times to work in the Appendix of a previous paper. 
	The gist of such results should (IMO) be summarised here.}
	\\
	\alert{We have added a summary of the different results derived in the previous paper.}
	
	\item 
	\textit{This readability issue is not made easier by the authors' commendable focus on generality, which leaves the reader carrying a lot of variables and ideas in their head. 
	Fine for a long paper, not so much for a Letter.}
	
	\item 
	\textit{My first suggestion to the authors would be to change from describing things in terms of a generic method "Y" to using a specific case [e.g. CCSD(T)] and then generalizing only at the end, e.g., "Of course, the above holds true for any method that provides a good approximation to the energy, not just CCSD(T).". 
	Other changes along these lines would probably also be useful. 
	This would help the reader cement the key concept (basis correction) without worrying about quite so many variables.}
	\\
	\alert{As proposed by the reviewer, we have explicitly specified the methods X and Y we employ here and left for the end the generalization to any method.}	
		
	\item 
	\textit{On a related note, I do not see the benefit of reporting the LDA correction in the main text, although for sure it belongs in the SI. 
	There seems to be no practical reason to do LDA when it just as expensive (??) as GGA, but gives worse results. 
	This would have the added advantage of reducing discussion on outcomes. 
	I kind of understand why the authors report LDA, but think it is a distraction since they have PBE.}
	\\
	\alert{We have moved the description and discussion of the LDA functional to the SI.}	
		
	\item 
	\textit{What I think would be very useful is to show $\mu(\bm{r})$ for an example, e.g. along the bond in an interesting diatom. 
	This would illustrate the range of values taken by $\mu$, and the advantage of doing things point-by-point. 
	If values for multiple basis sets were reported it might also help in understanding how and where larger basis sets help, which might point to how to improve basis sets in a more systematic fashion. 
	Removing the discussion on LDA would probably free enough space to show this, especially if Figure 2 was condensed into a single figure (which should be feasible sans LDA).}
	\\
	\alert{This is for Manu!}	
		
	\item 
	\textit{One final (minor) key point is that the proposed use of density fitting or related time-saving steps seems rather ambitious, given that it necessarily introduces a further basis set dependence. 
	I would suggest the authors do not mention the last sentence in the relevant paragraph, or give more detail if it is included.}
	\\
	\alert{Following the reviewer's advice, we have removed our comment on density-fitting and related methods.}	
		
	\item 
	\textit{Regardless of my issues with presentation, this is important work which should definitely be published in JPCL. 
	It just first needs to be made a bit easier to follow.}
	\\
	\alert{We would like to thank the reviewer for these supportive comments.}	
	
\end{itemize}

\newpage

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

	\textit{This is an excellent paper on density-based basis-set corrections for accelerating the basis-set convergence of an arbitrary wavefunction method. 
	The corrections are examined for the atomization and correlation energies of the G2 set of molecules. 
	In wavefunction theory, F12 methods have been developed in the 2000s. 
	The approach described in this paper provides a fast alternative to F12 that requires relatively large auxiliary basis functions for computing three- and four-electron integrals. 
	As a small notice, I suggest the the following for an update of reviews on F12, Grueneis et al., J. Chem. Phys., 146, 080901 (2017), Ma and Werner, WIREs Comput. Mol. Sci., 8:e1371 (2018).
	To summarize, I think this is an excellent paper that should be published in JPCL basically in the present form.}

	\alert{We would like to thank the reviewer for his/her kinds comments.
	We have added the two references suggested by the reviewer in due place.}

\end{letter}
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