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\documentclass[10pt]{letter}


\makeatletter


\newenvironment{thebibliography}[1]


{\list{\@biblabel{\@arabic\c@enumiv}}%


{\settowidth\labelwidth{\@biblabel{#1}}%


\leftmargin\labelwidth


\advance\leftmargin\labelsep


\usecounter{enumiv}%


\let\p@enumiv\@empty


\renewcommand\theenumiv{\@arabic\c@enumiv}}%


\sloppy


\clubpenalty4000


\@clubpenalty \clubpenalty


\widowpenalty4000%


\sfcode`\.\@m}


{\def\@noitemerr


{\@latex@warning{Empty `thebibliography' environment}}%


\endlist}


\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}


\makeatother




\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 fixednode 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 nonvariational mixed estimator is used for the


FNDMC 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 nonvariational mixed estimator is not used for the FNDMC energy


in this work.


}




\alert{


To clarify this point, we have added a sentence to the paper:


``With such parameters, both the timestep error and the bias due to the


finite projecting time are smaller than the error bars.''


}






%%% 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 multireference character. Indeed, as the authors pointed out,


the G1 set is only weakly correlated, and RSDFTCIPSI does not show its


best performances, and does not pay off. Indeed, in the G1 set, basisset


effects on the nodal surface quality seem to be more important than the


effect of dealing with a multireference wave function.






\alert{\textbf{Response:}


We totally agree with the reviewer that this method would perform even better


with strongly correlated systems. But in cases such as


the G1 set, although the total FNDMC energies are extremely low with CIPSI


trial wave functions, the energy differences are difficult to control. This is


even more true when the systems become large, and


this was a limit of the use of CIPSI wave functions for


QMC. Here, we have shown that this gap can be filled with the proposed


method. We believe that applying the RSDFTCIPSI to strongly


correlated systems is indeed an interesting topic, but it goes a bit


beyond the scope of the present manuscript and we prefer to leave the


study RSDFTCIPSI trial wave functions on strongly correlated systems


for a next study.


}








\bibliographystyle{unsrt}


\bibliography{ResponseLetter}


\end{letter}


\end{document}


















\documentclass[10pt]{letter}


\usepackage{UPS_letterhead,color,mhchem,mathpazo,ragged2e}


\newcommand{\alert}[1]{\textcolor{red}{#1}}




\makeatletter


\newenvironment{thebibliography}[1]


{\list{\@biblabel{\@arabic\c@enumiv}}%


{\settowidth\labelwidth{\@biblabel{#1}}%


\leftmargin\labelwidth


\advance\leftmargin\labelsep


\usecounter{enumiv}%


\let\p@enumiv\@empty


\renewcommand\theenumiv{\@arabic\c@enumiv}}%


\sloppy


\clubpenalty4000


\@clubpenalty \clubpenalty


\widowpenalty4000%


\sfcode`\.\@m}


{\def\@noitemerr


{\@latex@warning{Empty `thebibliography' environment}}%


\endlist}


\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}


\makeatother






\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 fixednode 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 nonvariational mixed estimator is used for the


FNDMC 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 nonvariational mixed estimator is not used for the FNDMC energy


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_Hetherington_1984,1998,Sorella_2000}


It is smart algorithm mixing pure diffusion Monte Carlo (PDMC) and DMC


and taking the best of those 2 methods~: 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.


The SR algorithm has 2 limits: with a single walker it falls back to


PDMC, and with an infinite population the DMC is recovered. The mixing


of the 2 methods does not introduce the population control bias of


DMC, and requires a much shorter projecting time than 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.


}




\alert{


To clarify this point, we have added a sentence to the paper:


\quote{


With such parameters, both the timestep error and the bias due to the


finite projecting time are smaller than the error bars.


}


}






%%% 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 multireference character. Indeed, as the authors pointed out,


the G1 set is only weakly correlated, and RSDFTCIPSI does not show its


best performances, and does not pay off. Indeed, in the G1 set, basisset


effects on the nodal surface quality seem to be more important than the


effect of dealing with a multireference wave function.






\alert{\textbf{Response:}


We totally agree with the reviewer, CIPSI trial wave functions can


handle very well multiconfigurational effects. In cases such as


the G1 set, although the total FNDMC energies are extremely low the


energy differences are difficult to control, especially for large


systems. This was a limit of the use of CIPSI wave functions for


QMC. Here, we have shown that this gap can be filled with the proposed


method. We believe that using RSDFTCIPSI in the context of strongly


correlated systems is indeed an interesting topic, but it goes a bit


beyond the scope of the present manuscript. Of course, we intend to


study RSDFTCIPSI trial wave functions on strongly correlated systems


in a near future.


}








\bibliographystyle{unsrt}


\bibliography{ResponseLetter}


\end{letter}


\end{document}













@ 457,11 +457,12 @@ the pseudopotential is localized. Hence, in the DLA, the fixednode


energy is independent of the Jastrow factor, as in allelectron


calculations. Simple Jastrow factors were used to reduce the


fluctuations of the local energy (see Sec.~\ref{sec:rsdftj} for their explicit expression).


The FNDMC simulations are performed with allelectron moves using the


\alert{The FNDMC simulations are performed with allelectron moves using the


stochastic reconfiguration algorithm developed by Assaraf \textit{et al.}


\cite{Assaraf_2000} with a time step of $5 \times 10^{4}$ a.u. and a


projecting time of $1$ a.u. \alert{With such parameters, both the


timestep error and the bias due to the finite projecting time are


\cite{Assaraf_2000} with a time step of $5 \times 10^{4}$ a.u.,


independent populations of 100 walkers and a projecting time of $1$


a.u. With such parameters, both the timestep error and the


bias due to the finite projecting time are


smaller than the error bars.}




All the data related to the present study (geometries, basis sets, total energies, \textit{etc}) can be found in the {\SI}.



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