corrections all around
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@ 21,14 +21,14 @@ decoration={snake,


\begin{tikzpicture}[scale=2.3]


\begin{scope}[very thick


,node distance=2cm,on grid,>=stealth'


,Op1/.style={circle,draw,fill=yellow!40}


,Ring1/.style={circle,draw,fill=red!40}


,Ring2/.style={circle,draw,fill=blue!40}


,Ring12/.style={circle,draw,fill=purple!40}


,Op1/.style={rectangle,draw,fill=yellow!40}


,Ring1/.style={rectangle,draw,fill=red!40}


,Ring2/.style={rectangle,draw,fill=blue!40}


,Ring12/.style={rectangle,draw,fill=purple!40}


,Ring1Test/.style={diamond,draw,fill=red!40}


,Ring12Test/.style={diamond,draw,fill=purple!40}


,Output/.style={ellipse,draw,fill=orange!40}


,Input/.style={rectangle,draw,fill=green!40}


,Input/.style={circle,draw,fill=green!40}


]


\node [Input, align=center] (H) at (3.052250,2.221211) { $\Psi^{(0)}$ };


\node [Op1, align=center] (He) at (2.258396,0.948498) { Compute \\ one$e$ \\ density };


@ 50,18 +50,18 @@ decoration={snake,


\path


(H) edge [>,color=black ] node [above,black] {} (He)


(He) edge [>,color=black ] node [above,black] { $n^{(0)}$ } (Li)


(Li) edge [>,color=black ] node [below,black,sloped,align=left] { $H^{\mu\,(k)}$ }


(Li) edge [>,color=black ] node [below,black,sloped,align=left] { $\hat{H}^{\mu\,(k)}$ }


node [above,black,sloped] { $k\leftarrow 0$ }(Be)


(Be) edge [>,color=black ] node [above,sloped,black] { $\Psi^{\mu\,(k)}$ } (B)


(Al) edge [>,color=black ] node [above,sloped,black] { no} (Be)


(B) edge [>,color=black ] node [below,sloped,black] { $n^{(k)}$ } (C)


(C) edge [>,color=black ] node [below,sloped,black] { $\tilde{n}^{(k)}$ } (N)


(N) edge [>,color=black ] node [below,sloped,black] { $H^{\mu\,(k,l)}$ }


(N) edge [>,color=black ] node [below,sloped,black] { $\hat{H}^{\mu\,(k)}$ }


node [above,sloped,black] { $l\leftarrow 0$ } (O)


(O) edge [>,color=black ] node [below,sloped,black] { $\Psi^{\mu\,(k,l)}$ }(F)


(F) edge [>,color=black ] node [below,sloped,black] { $n^{(k,l)}$ } (Ne)


(Ne) edge [>,color=black ] node [above,sloped,black] { $\tilde{n}^{(k,l)}$ } (Na)


(Na) edge [>,color=black ] node [above,sloped,black] { $E^{(k,l)}$ } (Mg)


(Na) edge [>,color=black ] node [above,sloped,black] { $\hat{H}^{\mu\,(k,l)}$ } (Mg)


(Mg) edge [>,color=black ] node [right,black] { yes } (Al)


(Mg) edge [>,color=black ] node [right,black] { no } (O)


(Al) edge [>,color=black ] node [above,sloped,black] {yes} (Si)



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@ 245,8 +245,8 @@ Considering that the perturbatively corrected energy is a reliable


estimate of the FCI energy, using a fixed value of the PT2 correction


as a stopping criterion enforces a constant distance of all the


calculations to the FCI energy. In this work, we target the chemical


accuracy so all the CIPSI selections were made such that $\EPT <


1$~m\hartree{}.


accuracy so all the CIPSI selections were made such that $\abs{\EPT} <


1$ millihartree.








@ 357,15 +357,15 @@ use the CIPSI algorithm to perform approximate FCI calculations


with the RSDFT Hamiltonian $\hat{H}^\mu$. \cite{GinPraFerAssSavTouJCP18}


This provides a multideterminant trial wave function $\Psi^{\mu}$ that one can ``feed'' to DMC.


In the outer (macroiteration) loop (red), at the $k$th iteration, a CIPSI selection is performed


to obtain $\Psi^{\mu\,(k)}$ with the RS Hamiltonian $\hat{H}^{\mu\,(k)}$


to obtain $\Psi^{\mu\,(k)}$ with the RSDFT Hamiltonian $\hat{H}^{\mu\,(k)}$


parameterized using the current oneelectron density $n^{(k)}$.


At each iteration, the number of determinants in $\Psi^{\mu\,(k)}$ increases.


One exits the outer loop when the absolute energy difference between two successive macroiterations $\Delta E^{(k)}$ is below a threshold $\tau_1$ that has been set to \titou{???} in the present study.


One exits the outer loop when the absolute energy difference between two successive macroiterations $\Delta E^{(k)}$ is below a threshold $\tau_1$ that has been set to $10^{3}$ hartree in the present study which is consistent with the CIPSI threshold (see Sec.~\ref{sec:compdetails}).


An inner (microiteration) loop (blue) is introduced to accelerate the


convergence of the selfconsistent calculation, in which the set of


determinants in $\Psi^{\mu\,(k,l)}$ is kept fixed, and only the diagonalization of


$\hat{H}^{\mu\,(k,l)}$ is performed iteratively with the updated density $n^{(k,l)}$.


The inner loop is exited when the absolute energy difference between two successive microiterations $\Delta E^{(k,l)}$ is below a threshold $\tau_2$ that has been here set to \titou{???}.


The inner loop is exited when the absolute energy difference between two successive microiterations $\Delta E^{(k,l)}$ is below a threshold $\tau_2$ that has been here set to $10^{2} \times \tau_1$ hartree.


The convergence of the algorithm was further improved


by introducing a direct inversion in the iterative subspace (DIIS)


step to extrapolate the density both in the outer and inner loops. \cite{Pulay_1980,Pulay_1982}


@ 391,12 +391,12 @@ CCSD(T) and KSDFT energies have been computed with




All the CIPSI calculations have been performed with \emph{Quantum


Package}.\cite{Garniron_2019,qp2_2020} We used the shortrange version


of the PerdewBurkeErnzerhof (PBE) \cite{PerBurErnPRL96} exchange


of \titou{the localdensity approximation (LDA)} and PerdewBurkeErnzerhof (PBE) \cite{PerBurErnPRL96} exchange


and correlation functionals defined in


Ref.~\onlinecite{GolWerStoLeiGorSavCP06} (see also


Refs.~\onlinecite{TouColSavJCP05,GolWerStoPCCP05}).


The convergence criterion for stopping the CIPSI calculations


has been set to $\EPT < 1$~m\hartree{} or $ \Ndet > 10^7$.


has been set to $\EPT < 10^{3}$ hartree or $ \Ndet > 10^7$.


All the wave functions are eigenfunctions of the $\Hat{S}^2$ spin operator, as


described in Ref.~\onlinecite{Applencourt_2018}.




@ 413,8 +413,6 @@ algorithm developed by Assaraf \textit{et al.}, \cite{Assaraf_2000}


with a time step of $5 \times 10^{4}$ a.u.


\titou{Allelectron move DMC?}




\titou{Missing details and references about srLDA and srPBE functionals.}




\section{Influence of the rangeseparation parameter on the fixednode


error}


\label{sec:mudmc}


@ 526,7 +524,7 @@ of $\Psi^J$ may be better than that of the FCI wave function, and therefore, we


To do so, we have made the following numerical experiment.


First, we extract the 200 determinants with the largest weights in the FCI wave


function out of a large CIPSI calculation. Within this set of determinants,


we solve the selfconsistent equations of RSDFT (see Eq.~\eqref{rsdfteigenequation})


we solve the selfconsistent equations of RSDFT [see Eq.~\eqref{rsdfteigenequation}]


with different values of $\mu$. This gives the CI expansions $\Psi^\mu$.


Then, within the same set of determinants we optimize the CI coefficients in the presence of


a simple one and twobody Jastrow factor. This gives the CI expansion $\Psi^J$.


@ 541,7 +539,7 @@ $\Psi^\mu$ together with that of $\Psi^J$.


\centering


\includegraphics[width=\columnwidth]{overlap.pdf}


\caption{\ce{H2O}, doublezeta basis set, 200 most important


determinants of the FCI expansion (see \ref{sec:rsdftj}).


determinants of the FCI expansion (see Sec.~\ref{sec:rsdftj}).


Overlap of the RSDFT CI expansions $\Psi^\mu$ with the CI


expansion optimized in the presence of a Jastrow factor $\Psi^J$.}


\label{fig:overlap}



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