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\usepackage{UPS_letterhead,color,mhchem,mathpazo,ragged2e}
\newcommand{\alert}[1]{\textcolor{red}{#1}}

\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 
{\it ``Taming the fixed-node error in diffusion Monte Carlo via range separation''}.
We would like 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 JCP.

We look forward to hearing from you.

\closing{Sincerely, the authors.}

\newpage

%%% REVIEWER 1 %%%
\noindent \textbf{\large Reviewer \#1}

It is assumed that the non-variational mixed estimator is used for the
FN-DMC energy. How adequate is the discussion on the error using a
lower energy in this case? Please elaborate this in detail.

\alert{\textbf{Response:} 
The DMC algorithm is stable at the cost of the introduction of a finite
population bias, and the PDMC algorithm is stabilized by introducing a finite
projecting time.
In this work, we have used the variant of Assaraf, Caffarel and
Khelif \cite{Assaraf_2000} (ref 112 in the paper) of the stochastic
reconfiguration (SR) algorithm developped by Hetherington and
Sorella \cite{Sorella_1998,Hetherington_1984,Sorella_2000}.
It is an algorithm mixing pure diffusion Monte Carlo (PDMC) with DMC, such that 
the mixing does not introduce the population control bias of DMC, and requires a
much shorter projecting time than PDMC.
In the limit of an infinite population the DMC is recovered, and
in the limit of a single walker it falls back to PDMC.
In practice, it is quite easy to reach a regime where the number of walkers and
the projecting time are such that the simulation is stable, the bias due to the
finite projecting time is negligible and the fluctuations introduced by the
projection are small.
So the non-variational mixed estimator has not been used for the FN-DMC energy
in this work.
}

\alert{
To clarify this point, we have added a sentence to the paper:
``With such parameters, both the time-step error and the bias due to the
finite projecting time are smaller than the error bars.''
}

\bibliographystyle{unsrt}
\bibliography{ResponseLetter}

%%% REVIEWER 2 %%%
\textbf{\large Reviewer \#2}

	
The only criticism I have is about the examples reported. Despite the
importance of the G1 test set, for which the atomization energies have
been computed, I would like to see an example where the ground state
has a true multi-reference character. Indeed, as the authors pointed out,
the G1 set is only weakly correlated, and RS-DFT-CIPSI does not show its
best performances, and does not pay off. Indeed, in the G1 set, basis-set
effects on the nodal surface quality seem to be more important than the
effect of dealing with a multi-reference wave function.


\alert{\textbf{Response:} 
We agree with the reviewer that the present method would perform even better
with strongly correlated systems. However, for systems such as
the ones gathered in the G1 set, although the total FN-DMC energies are extremely low with CIPSI
trial wave functions, energy differences are difficult to control. 
This comment is also valid when systems get large, and 
this was a clear limitation of the use of CIPSI trial wave functions within QMC.
We have shown that this problem can be alleviated with the here-proposed method which combines RS-DFT and CIPSI. 
We believe that applying the RS-DFT-CIPSI scheme to strongly
correlated systems is indeed an interesting topic, but it clearly goes
beyond the scope of the present manuscript.
Consequently, we prefer to leave the study of RS-DFT-CIPSI trial wave functions on strongly correlated systems for a future work.
This has been mentioned in the concluding section of the revised manuscript.
}



\end{letter}
\end{document}






