2020-09-22 13:06:28 +02:00
|
|
|
\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 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
|
2020-09-22 13:19:54 +02:00
|
|
|
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}.
|
2020-09-22 13:06:28 +02:00
|
|
|
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.
|
2020-09-22 13:19:54 +02:00
|
|
|
So the non-variational mixed estimator has not been used for the FN-DMC energy
|
2020-09-22 13:06:28 +02:00
|
|
|
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.''
|
|
|
|
}
|
|
|
|
|
2020-09-22 14:06:39 +02:00
|
|
|
\bibliographystyle{unsrt}
|
|
|
|
\bibliography{ResponseLetter}
|
2020-09-22 13:06:28 +02:00
|
|
|
|
|
|
|
%%% 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:}
|
2020-09-22 13:19:54 +02:00
|
|
|
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.
|
2020-09-22 14:06:39 +02:00
|
|
|
Consequently, we prefer to leave the study of RS-DFT-CIPSI trial wave functions on strongly correlated systems for a future work.
|
2020-09-22 13:19:54 +02:00
|
|
|
This has been mentioned in the concluding section of the revised manuscript.
|
2020-09-22 13:06:28 +02:00
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
\end{letter}
|
|
|
|
\end{document}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|