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Response_Letter/ResponseLetter.tex Normal file
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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 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 is not 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.''
}
%%% 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 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 FN-DMC 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 RS-DFT-CIPSI 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 RS-DFT-CIPSI 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 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 non-variational mixed estimator is not used for the FN-DMC 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 time-step 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 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 totally agree with the reviewer, CIPSI trial wave functions can
handle very well multi-configurational effects. In cases such as
the G1 set, although the total FN-DMC 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 RS-DFT-CIPSI 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 RS-DFT-CIPSI trial wave functions on strongly correlated systems
in a near future.
}
\bibliographystyle{unsrt}
\bibliography{ResponseLetter}
\end{letter}
\end{document}

9
Revision/rsdft-cipsi-qmc.tex
View File

@ -457,11 +457,12 @@ the pseudopotential is localized. Hence, in the DLA, the fixed-node
energy is independent of the Jastrow factor, as in all-electron
calculations. Simple Jastrow factors were used to reduce the
fluctuations of the local energy (see Sec.~\ref{sec:rsdft-j} for their explicit expression).
The FN-DMC simulations are performed with all-electron moves using the
\alert{The FN-DMC simulations are performed with all-electron 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
time-step 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 time-step 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}.