122 lines
4.6 KiB
TeX
122 lines
4.6 KiB
TeX
\documentclass[10pt]{letter}
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\makeatletter
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\newenvironment{thebibliography}[1]
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{\list{\@biblabel{\@arabic\c@enumiv}}%
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{\settowidth\labelwidth{\@biblabel{#1}}%
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\leftmargin\labelwidth
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\advance\leftmargin\labelsep
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\usecounter{enumiv}%
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\let\p@enumiv\@empty
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\renewcommand\theenumiv{\@arabic\c@enumiv}}%
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\sloppy
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\clubpenalty4000
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\@clubpenalty \clubpenalty
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\widowpenalty4000%
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\sfcode`\.\@m}
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{\def\@noitemerr
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{\@latex@warning{Empty `thebibliography' environment}}%
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\endlist}
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\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
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\makeatother
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\usepackage{UPS_letterhead,color,mhchem,mathpazo,ragged2e}
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\newcommand{\alert}[1]{\textcolor{red}{#1}}
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\begin{document}
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\begin{letter}%
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{To the Editors of the Journal of Chemical Physics}
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\opening{Dear Editors,}
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\justifying
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Please find attached a revised version of the manuscript entitled
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{\it ``Taming the fixed-node error in diffusion Monte Carlo via range separation''}.
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We would like to thank the reviewers for their constructive comments.
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Our detailed responses to their comments can be found below.
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For convenience, all modifications and changes are highlighted in red in the revised version of the manuscript.
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We hope that you will agree that our manuscript is now suitable for publication in JCP.
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We look forward to hearing from you.
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\closing{Sincerely, the authors.}
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\newpage
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%%% REVIEWER 1 %%%
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\noindent \textbf{\large Reviewer \#1}
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It is assumed that the non-variational mixed estimator is used for the
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FN-DMC energy. How adequate is the discussion on the error using a
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lower energy in this case? Please elaborate this in detail.
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\alert{\textbf{Response:}
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The DMC algorithm is stable at the cost of the introduction of a finite
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population bias, and the PDMC algorithm is stabilized by introducing a finite
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projecting time.
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In this work, we have used the variant of Assaraf, Caffarel and
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Khelif \cite{Assaraf_2000} (ref 112 in the paper) of the stochastic
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reconfiguration (SR) algorithm developped by Hetherington and
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Sorella \cite{Sorella_1998,Hetherington_1984,Sorella_2000}.
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It is an algorithm mixing pure diffusion Monte Carlo (PDMC) with DMC, such that
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the mixing does not introduce the population control bias of DMC, and requires a
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much shorter projecting time than PDMC.
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In the limit of an infinite population the DMC is recovered, and
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in the limit of a single walker it falls back to PDMC.
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In practice, it is quite easy to reach a regime where the number of walkers and
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the projecting time are such that the simulation is stable, the bias due to the
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finite projecting time is negligible and the fluctuations introduced by the
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projection are small.
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So the non-variational mixed estimator has not been used for the FN-DMC energy
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in this work.
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}
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\alert{
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To clarify this point, we have added a sentence to the paper:
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``With such parameters, both the time-step error and the bias due to the
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finite projecting time are smaller than the error bars.''
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}
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\bibliographystyle{unsrt}
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\bibliography{ResponseLetter}
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%%% REVIEWER 2 %%%
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\textbf{\large Reviewer \#2}
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The only criticism I have is about the examples reported. Despite the
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importance of the G1 test set, for which the atomization energies have
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been computed, I would like to see an example where the ground state
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has a true multi-reference character. Indeed, as the authors pointed out,
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the G1 set is only weakly correlated, and RS-DFT-CIPSI does not show its
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best performances, and does not pay off. Indeed, in the G1 set, basis-set
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effects on the nodal surface quality seem to be more important than the
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effect of dealing with a multi-reference wave function.
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\alert{\textbf{Response:}
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We agree with the reviewer that the present method would perform even better
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with strongly correlated systems. However, for systems such as
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the ones gathered in the G1 set, although the total FN-DMC energies are extremely low with CIPSI
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trial wave functions, energy differences are difficult to control.
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This comment is also valid when systems get large, and
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this was a clear limitation of the use of CIPSI trial wave functions within QMC.
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We have shown that this problem can be alleviated with the here-proposed method which combines RS-DFT and CIPSI.
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We believe that applying the RS-DFT-CIPSI scheme to strongly
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correlated systems is indeed an interesting topic, but it clearly goes
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beyond the scope of the present manuscript.
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Consequently, we prefer to leave the study of RS-DFT-CIPSI trial wave functions on strongly correlated systems for a future work.
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This has been mentioned in the concluding section of the revised manuscript.
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}
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\end{letter}
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\end{document}
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