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Pierre-Francois Loos 2020-09-22 13:19:54 +02:00
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32
Response_Letter/ResponseLetter.tex
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@ -55,9 +55,9 @@ 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 population bias, and the PDMC algorithm is stabilized by introducing a finite
projecting time. projecting time.
In this work, we have used the variant of Assaraf, Caffarel and In this work, we have used the variant of Assaraf, Caffarel and
Khelif\cite{Assaraf_2000} (ref 112 in the paper) of the Stochastic Khelif \cite{Assaraf_2000} (ref 112 in the paper) of the stochastic
Reconfiguration (SR) algorithm developped by Hetherington and reconfiguration (SR) algorithm developped by Hetherington and
Sorella.\cite{Sorella_1998,Hetherington_1984,Sorella_2000} Sorella \cite{Sorella_1998,Hetherington_1984,Sorella_2000}.
It is an algorithm mixing pure diffusion Monte Carlo (PDMC) with DMC, such that 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 the mixing does not introduce the population control bias of DMC, and requires a
much shorter projecting time than PDMC. much shorter projecting time than PDMC.
@ -67,7 +67,7 @@ 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 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 finite projecting time is negligible and the fluctuations introduced by the
projection are small. projection are small.
So the non-variational mixed estimator is not used for the FN-DMC energy So the non-variational mixed estimator has not been used for the FN-DMC energy
in this work. in this work.
} }
@ -93,18 +93,18 @@ effect of dealing with a multi-reference wave function.
\alert{\textbf{Response:} \alert{\textbf{Response:}
We totally agree with the reviewer that this method would perform even better We agree with the reviewer that the present method would perform even better
with strongly correlated systems. But in cases such as with strongly correlated systems. However, for systems such as
the G1 set, although the total FN-DMC energies are extremely low with CIPSI the ones gathered in 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 trial wave functions, energy differences are difficult to control.
even more true when the systems become large, and This comment is also valid when systems get large, and
this was a limit of the use of CIPSI wave functions for this was a clear limitation of the use of CIPSI trial wave functions within QMC.
QMC. Here, we have shown that this gap can be filled with the proposed We have shown that this problem can be alleviated with the here-proposed method which combines RS-DFT and CIPSI.
method. We believe that applying the RS-DFT-CIPSI to strongly We believe that applying the RS-DFT-CIPSI scheme to strongly
correlated systems is indeed an interesting topic, but it goes a bit correlated systems is indeed an interesting topic, but it clearly goes
beyond the scope of the present manuscript and we prefer to leave the beyond the scope of the present manuscript.
study RS-DFT-CIPSI trial wave functions on strongly correlated systems Consequently, we prefer to leave the study RS-DFT-CIPSI trial wave functions on strongly correlated systems for a future study.
for a next study. This has been mentioned in the concluding section of the revised manuscript.
} }

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Revision/rsdft-cipsi-qmc.tex
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@ -992,6 +992,8 @@ value of $\mu$ can be further reduced to $0.25$~bohr$^{-1}$ to get
extremely compact wave functions at the price of less efficient extremely compact wave functions at the price of less efficient
cancellations of errors. cancellations of errors.
\alert{We hope to report, in the near future, a detailed investigation of strongly-correlated systems with the present RS-DFT-CIPSI scheme.}
%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%
\begin{acknowledgments} \begin{acknowledgments}
A.B was supported by the U.S.~Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials. A.B was supported by the U.S.~Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, as part of the Computational Materials Sciences Program and Center for Predictive Simulation of Functional Materials.