minor corrections
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@ 623,7 +623,7 @@ $\Psi^\mu$ together with that of $\Psi^J$.


\centering


\includegraphics[width=\columnwidth]{h2o200dmc.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}).


FNDMC energies of $\Psi^\mu$ (red curve), together with


the FNDMC energy of $\Psi^J$ (blue line). The width of the lines


represent the statistical error bars.}


@ 641,7 +641,8 @@ an impact on the CI coefficients similar to the Jastrow factor.


%%% TABLE II %%%


\begin{table}


\caption{\ce{H2O}, doublezeta basis set. Integrated ontop pair density $\expval{ n_2(\br,\br) }$


for $\Psi^J$ and $\Psi^\mu$ with different values of $\mu$. }


for $\Psi^J$ and $\Psi^\mu$ with different values of $\mu$.


\titou{Please remove table and merge data in the Fig. 5.}}


\label{table_on_top}


\begin{ruledtabular}


\begin{tabular}{cc}


@ 665,7 +666,7 @@ an impact on the CI coefficients similar to the Jastrow factor.


\begin{figure}


\centering


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


\caption{\ce{H2O}, doublezeta basis set. Density $n(\br)$ along


\caption{\ce{H2O}, \titou{srLDA?} doublezeta basis set. Oneelectron density $n(\br)$ along


the \ce{OH} axis, for $\Psi^J$ (dashed curve) and $\Psi^\mu$ with different values of $\mu$. }


\label{fig:n1}


\end{figure}


@ 676,7 +677,7 @@ an impact on the CI coefficients similar to the Jastrow factor.


\begin{figure}


\centering


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


\caption{\ce{H2O}, doublezeta basis set. Ontop pair


\caption{\ce{H2O}, \titou{srLDA?} doublezeta basis set. Ontop pair


density $n_2(\br,\br)$ along the \ce{OH} axis,


for $\Psi^J$ (dashed curve) and $\Psi^\mu$ with different values of $\mu$. }


\label{fig:n2}


@ 693,7 +694,7 @@ report in Table~\ref{table_on_top} the integrated ontop pair density


where $n_2(\br_1,\br_2)$ is the twobody density [normalized to $N(N1)$ where $N$ is the number of electrons]


obtained for both $\Psi^\mu$ and $\Psi^J$.


Then, in order to have a pictorial representation of both the ontop


pair density and the density, we report in Fig.~\ref{fig:n1} and Fig.~\ref{fig:n2}


pair density and the density, we report in Figs.~\ref{fig:n1} and \ref{fig:n2}


the plots of the total density $n(\br)$ and ontop pair density


$n_2(\br,\br)$ along one \ce{OH} axis of the water molecule.




@ 726,7 +727,7 @@ increases the probability to find electrons at short distances in $\Psi^\mu$,


while the effective onebody potential $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n_{\Psi^{\mu}}]$,


provided that it is exact, maintains the exact onebody density.


This is clearly what has been observed from the plots in


Fig.~\ref{fig:n1} and Fig.~\ref{fig:n2}.


Figs.~\ref{fig:n1} and \ref{fig:n2}.


Regarding now the transcorrelated Hamiltonian $e^{J}He^J$, as pointed out by TenNo,\cite{Tenno2000Nov}


the effective twobody interaction induced by the presence of a Jastrow factor


can be nondivergent when a proper Jastrow factor is chosen.


@ 814,7 +815,7 @@ Another source of sizeconsistency error in QMC calculations originates


from the Jastrow factor. Usually, the Jastrow factor contains


oneelectron, twoelectron and onenucleustwoelectron terms.


The problematic part is the twoelectron term, whose simplest form can


be expressed as in Eq.\eqref{eq:jastee}.


be expressed as in Eq.~\eqref{eq:jastee}.


The parameter


$a$ is determined by cusp conditions, and $b$ is obtained by energy


or variance minimization.\cite{Coldwell_1977,Umrigar_2005}


@ 871,7 +872,7 @@ parameter.


We have computed the FNDMC energy of the dissociated fluorine dimer, where


the two atoms are at a distance of 50~\AA. We expect that the energy


of this system is equal to twice the energy of the fluorine atom.


The data in table~\ref{tab:sizecons} shows that it is indeed the


The data in Table~\ref{tab:sizecons} shows that it is indeed the


case, so we can conclude that the proposed scheme provides


sizeconsistent FNDMC energies for all values of $\mu$ (within


$2\times$ statistical error bars).


@ 927,11 +928,11 @@ In this section, we investigate the impact of the spin contamination


due to the shortrange density functional on the FNDMC energy. We have


computed the energies of the carbon atom in its triplet state


with BFD pseudopotentials and the corresponding doublezeta basis


set. The calculation was done with $m_s=1$ (3 $\uparrow$ electrons


and 1 $\downarrow$ electrons) and with $m_s=0$ (2 $\uparrow$ and 2


$\downarrow$ electrons).


set. The calculation was done with $m_s=1$ (3 spinup electrons


and 1 spindown electrons) and with $m_s=0$ (2 spinup and 2


spindown electrons).




The results are presented in table~\ref{tab:spin}.


The results are presented in Table~\ref{tab:spin}.


Although using $m_s=0$ the energy is higher than with $m_s=1$, the


bias is relatively small, more than one order of magnitude smaller


than the energy gained by reducing the fixednode error going from the single


@ 1070,7 +1071,7 @@ $\mu=0.5$~bohr$^{1}$ with the quadruplezeta basis set.




Searching for the optimal value of $\mu$ may be too costly, so we have


computed the MAD, MSE and RMSD for fixed values of $\mu$. The results


are illustrated in figure~\ref{fig:g2dmc}. As seen on the figure and


are illustrated in Fig.~\ref{fig:g2dmc}. As seen on the figure and


in Table~\ref{tab:mad}, the best choice for a fixed value of $\mu$ is


0.5~bohr$^{1}$ for all three basis sets. It is the value for which


the MAE (3.74(35), 2.46(18) and 2.06(35) kcal/mol) and RMSD (4.03(23),


@ 1094,7 +1095,7 @@ cancellations of errors.


%%% %%% %%% %%%




The number of determinants in the trial wave functions are shown in


figure~\ref{fig:g2ndet}. As expected, the number of determinants


Fig.~\ref{fig:g2ndet}. As expected, the number of determinants


is smaller when $\mu$ is small and larger when $\mu$ is large.


It is important to remark that the median of the number of


determinants when $\mu=0.5$~bohr$^{1}$ is below 100~000 determinants



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