minor corrections
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@ 23,7 +23,7 @@


\newcommand{\titou}[1]{\textcolor{red}{#1}}


\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}


\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}


\newcommand{\SI}{supplementary material}


\newcommand{\SI}{\textcolor{blue}{supplementary material}}




\newcommand{\mc}{\multicolumn}


\newcommand{\fnm}{\footnotemark}


@ 269,10 +269,10 @@ where


are the singular shortrange (sr) part and the nonsingular longrange (lr) part, respectively, $\mu$ is the rangeseparation parameter which controls how rapidly the shortrange part decays, $\erf(x)$ is the error function, and $\erfc(x) = 1  \erf(x)$ is its complementary version.




The main idea behind RSDFT is to treat the shortrange part of the


interaction within KSDFT, and the long range part within a WFT method like FCI in the present case.


interaction within KSDFT, and the longrange part within a WFT method like FCI in the present case.


The parameter $\mu$ controls the range of the separation, and allows


to go continuously from the KS Hamiltonian ($\mu=0$) to


the FCI Hamiltonian ($\mu = \infty$).


the FCI Hamiltonian ($\mu \to \infty$).




To rigorously connect WFT and DFT, the universal


LevyLieb density functional \cite{LevPNAS79,LieIJQC83} is


@ 295,7 +295,7 @@ electronic energy


},


\end{equation}


with $\hat{T}$ the kinetic energy operator,


$\hat{W}_\text{ee}^{\text{lr}}$ the longrange


$\hat{W}_\text{ee}^{\text{lr},\mu}$ the longrange


electronelectron interaction,


$n_\Psi$ the oneelectron density associated with $\Psi$,


and $\hat{V}_{\text{ne}}$ the electronnucleus potential.


@ 360,12 +360,12 @@ In the outer (macroiteration) loop (red), at the $k$th iteration, a CIPSI selec


to obtain $\Psi^{\mu\,(k)}$ with the RS 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 macroiteration loop when the absolute energy difference between two successive iterations $\Delta E^{(k)}$ 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 \titou{???} in the present study.


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 microiteration loop is exited when the absolute energy difference between two successive iterations $\Delta E^{(k,l)}$ is below a threshold $\tau_2$ that has been set to \titou{???} in the present study.


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 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}


@ 379,8 +379,8 @@ the final trial wave function $\Psi^{\mu}$ is independent of the starting wave f


\section{Computational details}


\label{sec:compdetails}




\titou{The geometries for the G2 data set are provided as {\SI}.}




For all the systems considered here, experimental geometries have been considered and they have been extracted from the NIST website.


Geometries for each system are reported in the {\SI}.




All the calculations have been performed using BurkatzkiFilippiDolg (BFD)


pseudopotentials \cite{Burkatzki_2007,Burkatzki_2008} with the associated double,


@ 413,6 +413,7 @@ 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}


@ 457,19 +458,19 @@ with a time step of $5 \times 10^{4}$ a.u.




The first question we would like to address is the quality of the


nodes of the wave functions $\Psi^{\mu}$ obtained with an intermediate


range separation parameter (\textit{i.e.} $0 < \mu < +\infty$).


We generated trial wave functions $\Psi^\mu$ with multiple values of


$\mu$, and computed the associated fixed node energy keeping all the


parameters having an impact on the nodal surface fixed.


We considered a weakly correlated molecular systems: the water


range separation parameter (\ie, $0 < \mu < +\infty$).


For this purpose, we consider a weakly correlated molecular system: the water


molecule near its equilibrium geometry.\cite{Caffarel_2016}


We then generate trial wave functions $\Psi^\mu$ for multiple values of


$\mu$, and compute the associated fixednode energy keeping all the


parameters having an impact on the nodal surface fixed (\titou{such as ??}).




\subsection{Fixednode energy of $\Psi^\mu$}


\label{sec:fndmc_mu}


From Table~\ref{tab:h2odmc} and Fig.~\ref{fig:h2odmc},


one can clearly observe that using a FCI trial


wave functions ($\mu = \infty$) give an FNDMC energies lower


than the energies obtained with a single KohnSham determinant ($\mu=0$):


one can clearly observe that using FCI trial


wave functions ($\mu \to \infty$) give FNDMC energies lower


than the energies obtained with a single KS determinant ($\mu=0$):


a gain of $3.2 \pm 0.6$~m\hartree{} at the doublezeta level and $7.2 \pm


0.3$~m\hartree{} at the triplezeta level are obtained.


Coming now to the nodes of the trial wave functions $\Psi^{\mu}$ with



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