modifs T2
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@ -55,9 +55,9 @@ 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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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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@ -67,7 +67,7 @@ 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 is not used for the FN-DMC energy
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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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@ -93,18 +93,18 @@ effect of dealing with a multi-reference wave function.
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\alert{\textbf{Response:}
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We totally agree with the reviewer that this method would perform even better
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with strongly correlated systems. But in cases such as
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the G1 set, although the total FN-DMC energies are extremely low with CIPSI
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trial wave functions, the energy differences are difficult to control. This is
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even more true when the systems become large, and
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this was a limit of the use of CIPSI wave functions for
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QMC. Here, we have shown that this gap can be filled with the proposed
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method. We believe that applying the RS-DFT-CIPSI to strongly
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correlated systems is indeed an interesting topic, but it goes a bit
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beyond the scope of the present manuscript and we prefer to leave the
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study RS-DFT-CIPSI trial wave functions on strongly correlated systems
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for a next study.
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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 RS-DFT-CIPSI trial wave functions on strongly correlated systems for a future study.
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This has been mentioned in the concluding section of the revised manuscript.
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}
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@ -992,6 +992,8 @@ value of $\mu$ can be further reduced to $0.25$~bohr$^{-1}$ to get
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extremely compact wave functions at the price of less efficient
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cancellations of errors.
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\alert{We hope to report, in the near future, a detailed investigation of strongly-correlated systems with the present RS-DFT-CIPSI scheme.}
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%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{acknowledgments}
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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.
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